935_E. Fafa and Ancient Mathematics_36808
Ancient Egyptians are known to have understood difficult concepts in mathematics. The ancient Egyptian mathematician Ahmes liked to write a kind of arithmetic expressions on papyrus paper which he called as Ahmes arithmetic expression.

An Ahmes arithmetic expression can be defined as: 

  * "d" is an Ahmes arithmetic expression, where d is a one-digit positive integer; 
  * "(E1 op E2)" is an Ahmes arithmetic expression, where E1 and E2 are valid Ahmes arithmetic expressions (without spaces) and op is either plus ( + ) or minus ( - ). 

For example 5, (1-1) and ((1+(2-3))-5) are valid Ahmes arithmetic expressions.

On his trip to Egypt, Fafa found a piece of papyrus paper having one of these Ahmes arithmetic expressions written on it. Being very ancient, the papyrus piece was very worn out. As a result, all the operators were erased, keeping only the numbers and the brackets. Since Fafa loves mathematics, he decided to challenge himself with the following task:

Given the number of plus and minus operators in the original expression, find out the maximum possible value for the expression on the papyrus paper after putting the plus and minus operators in the place of the original erased operators.

Input

The first line contains a string E (1 ≤ |E| ≤ 104) — a valid Ahmes arithmetic expression. All operators are erased and replaced with '?'.

The second line contains two space-separated integers P and M (0 ≤ min(P, M) ≤ 100) — the number of plus and minus operators, respectively. 

It is guaranteed that P + M =  the number of erased operators.

Output

Print one line containing the answer to the problem.

Examples

Input

(1?1)
1 0


Output

2


Input

(2?(1?2))
1 1


Output

1


Input

((1?(5?7))?((6?2)?7))
3 2


Output

18


Input

((1?(5?7))?((6?2)?7))
2 3


Output

16

Note

  * The first sample will be (1 + 1) = 2. 
  * The second sample will be (2 + (1 - 2)) = 1. 
  * The third sample will be ((1 - (5 - 7)) + ((6 + 2) + 7)) = 18. 
  * The fourth sample will be ((1 + (5 + 7)) - ((6 - 2) - 7)) = 16. 
from math import inf

class Node:
    def __init__(self, parent = None, leftExp = None, rightExp = None, signQ = 0):
        self.parent, self.leftExp, self.rightExp, self.signQ = parent, leftExp, rightExp, signQ
    def __str__(self):
        return "Node"

memo = {}

def Memoize(node, p, maxValue, minValue):
    if not node in memo:
        memo.update({node : {p : [maxValue, minValue]} })
    else:
        memo[node].update({p : [maxValue, minValue]})

def ExpMaxValue(root: Node, p):

    m = root.signQ - p
    """if root.signQ == 1:
        if p == 1:
            return [root.leftExp.value + root.rightExp.value, root.leftExp.value + root.rightExp.value]
        else:
            return [root.leftExp.value - root.rightExp.value, root.leftExp.value - root.rightExp.value]"""

    if root.signQ == 0:
        return [root.value, root.value]
    
    if root in memo:
        if p in memo[root]:
            return memo[root][p]

    if m == 0:
        value = ExpMaxValue(root.leftExp, root.leftExp.signQ)[0] + ExpMaxValue(root.rightExp, root.rightExp.signQ)[0]
        Memoize(root, p, value, value)
        return [value, value]
    if p == 0:
        value = ExpMaxValue(root.leftExp, 0)[0] - ExpMaxValue(root.rightExp, 0)[0]
        Memoize(root, p, value, value)
        return [value, value]
        
    maxValue = -inf
    minValue = inf
    if m >= p:
        for pQMid in range(2):
            pQLeftMin = min(p - pQMid, root.leftExp.signQ)
            for pQLeft in range(pQLeftMin + 1):
                if root.leftExp.signQ - pQLeft + (1 - pQMid) > m:
                    continue
                
                resLeft = ExpMaxValue(root.leftExp, pQLeft)
                resRight = ExpMaxValue(root.rightExp, p - pQMid - pQLeft)
                
                if pQMid == 1:
                    maxValue = max(resLeft[0] + resRight[0], maxValue)
                    minValue = min(resLeft[1] + resRight[1], minValue)
                else:
                    maxValue = max(resLeft[0] - resRight[1], maxValue)
                    minValue = min(resLeft[1] - resRight[0], minValue)
    else:
        for mQMid in range(2):
            mQLeftMin = min(m - mQMid, root.leftExp.signQ)
            for mQLeft in range(mQLeftMin + 1):
                pQLeft = root.leftExp.signQ - mQLeft
                if pQLeft + (1 - mQMid) > p:
                    continue
                
                resLeft = ExpMaxValue(root.leftExp, pQLeft)
                resRight = ExpMaxValue(root.rightExp, p - (1 - mQMid) - pQLeft)
                
                if mQMid == 0:
                    maxValue = max(resLeft[0] + resRight[0], maxValue)
                    minValue = min(resLeft[1] + resRight[1], minValue)
                else:
                    maxValue = max(resLeft[0] - resRight[1], maxValue)
                    minValue = min(resLeft[1] - resRight[0], minValue)

    Memoize(root, p, int(maxValue), int(minValue))

    return [int(maxValue), int(minValue)]
                
                

def PrintNodes(root: Node):
    if root.signQ != 0:
        leftExp = root.leftExp if root.leftExp.signQ != 0 else root.leftExp.value
        rightExp = root.rightExp if root.rightExp.signQ != 0 else root.rightExp.value
        check = root.signQ == root.leftExp.signQ + root.rightExp.signQ + 1
        print(root.signQ, root.parent, leftExp, rightExp, check)
        PrintNodes(root.leftExp)
        PrintNodes(root.rightExp)

        

def main():
    exp = str(input())
    if len(exp) == 1:
        print(exp)
        return
    
    #root = Node(None, None, None)
    #root.parent = root
    cNode = Node()
    isRight = False
    
    for i in range(1, len(exp) - 1):
        if exp[i] == '(':
            if not isRight:
                cNode.leftExp = Node(cNode)
                cNode = cNode.leftExp
            else:
                cNode.rightExp = Node(cNode)
                cNode = cNode.rightExp
            isRight = False
        elif exp[i] == '?':
            isRight = True
            cNode.signQ += 1
        elif exp[i] == ')':
            if cNode.parent != None:
                cNode.parent.signQ += cNode.signQ
            cNode = cNode.parent
            isRight = False
        else:
            if not isRight:
                cNode.leftExp = Node(cNode)
                cNode.leftExp.value = int(exp[i])
            else:
                cNode.rightExp = Node(cNode)
                cNode.rightExp.value = int(exp[i])

    
    #PrintNodes(cNode)

    ss = str(input()).split()
    p, m = int(ss[0]), int(ss[1])

    print(ExpMaxValue(cNode, p)[0])
    


    

main()
((1?(5?7))?((6?2)?7))
3 2
 (1?1)
1 0
 ((1?(5?7))?((6?2)?7))
2 3
 (2?(1?2))
1 1
 (((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((4?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?2))?7)))))?4))?1)?7)
50 49
 8
0 0
 (((4?7)?(9?((6?(3?2))?((6?3)?7))))?((5?((7?(7?(8?3)))?(4?2)))?2))
16 0
 ((4?3)?(((2?(4?((4?((2?(3?(7?3)))?(((((3?(6?2))?3)?(((((6?6)?(1?5))?((8?8)?1))?(5?((7?((6?((((3?8)?8)?(8?5))?7))?8))?((8?(2?8))?3))))?6))?(8?(7?5)))?8)))?((((7?(4?3))?4)?5)?((1?(((2?2)?((((4?((7?6)?(1?4)))?(8?(1?(((1?3)?(((2?2)?(3?(8?(9?((2?(4?6))?(7?8))))))?(9?(7?9))))?(7?3)))))?((2?((2?((8?6)?1))?(3?1)))?(7?1)))?5))?((((6?(9?(((5?4)?7)?((5?8)?8))))?5)?7)?(2?2))))?4)))))?2)?(7?(4?((6?6)?6)))))
50 49
 ((((4?6)?9)?((5?(7?1))?(6?(4?(((((((7?3)?7)?(((((8?(6?7))?((1?2)?(5?8)))?8)?7)?4))?6)?7)?1)?((7?(2?((1?(((8?(((((2?7)?(((((3?6)?3)?(((((9?5)?7)?(1?(5?5)))?(8?((3?(1?2))?((8?5)?(7?((9?((9?8)?7))?1))))))?1))?1)?(9?2)))?((7?5)?((9?(4?(9?6)))?(8?(((5?7)?2)?(6?(3?8)))))))?(((4?(2?2))?(7?9))?((7?((((4?(3?(7?3)))?8)?3)?(5?(((9?2)?(9?((((2?(7?3))?(3?(1?(9?(6?(9?8))))))?2)?2)))?2))))?((9?((2?(2?3))?((9?((7?4)?1))?5)))?((((9?6)?3)?(4?1))?7)))))?5))?4)?4))?7)))?5))))))?1)
2 114
 ((((3?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?6)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))
100 12
 (9?((1?(3?(5?((9?7)?(((((4?5)?2)?1)?(7?6))?(3?(9?7)))))))?(1?4)))
0 16
 (4?(((3?2)?((((((4?(4?((2?3)?((7?((3?3)?(6?(((2?(3?6))?6)?(((1?5)?8)?(((8?1)?(5?7))?6))))))?(3?8)))))?((8?8)?5))?(7?(8?((((8?((((2?(8?(((3?6)?8)?7)))?5)?(8?(7?((4?(3?4))?(5?((1?(2?((2?(4?7))?(((6?1)?(4?(8?1)))?(1?(3?(((2?(2?(3?(8?9))))?(((((2?4)?6)?7)?(8?9))?7))?(((9?(7?3))?2)?((((((2?8)?6)?(1?3))?1)?7)?1)))))))))?(5?(6?(9?(5?4))))))))))?7))?5)?(8?(8?((5?7)?2))))?2))))?4)?(2?((7?4)?6)))?6))?6))
50 49
 ((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?6)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))
100 12
 ((1?(2?7))?((6?5)?7))
2 3
 (4?(((3?2)?((((((4?(4?((2?3)?((7?((3?3)?(6?(((2?(3?6))?6)?(((1?5)?8)?(((8?1)?(5?7))?6))))))?(3?8)))))?((8?8)?5))?(7?(8?((((8?((((2?(8?(((3?6)?8)?7)))?5)?(8?(7?((4?(3?4))?(5?((1?(2?((2?(4?7))?(((6?1)?(4?(8?1)))?(1?(3?(((2?(2?(3?(8?9))))?(((((2?4)?6)?7)?(8?9))?7))?(((9?(7?3))?2)?((((((2?8)?6)?(1?3))?1)?7)?1)))))))))?(5?(6?(9?(5?4))))))))))?7))?5)?(8?(8?((5?7)?2))))?2))))?4)?(1?((7?4)?6)))?6))?6))
50 49
 (2?(1?2))
0 2
 (2?(2?2))
0 2
 (2?2)
1 0
 (((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((5?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?2))?7)))))?4))?1)?7)
50 49
 ((1?(5?7))?((6?2)?6))
3 2
 (2?(1?2))
2 0
 ((1?(7?5))?((6?2)?7))
3 2
 ((1?(5?7))?((6?2)?8))
3 2
 (4?(((3?2)?((((((4?(4?((2?3)?((7?((3?3)?(6?(((2?(3?6))?6)?(((1?5)?8)?(((8?1)?(5?7))?6))))))?(3?8)))))?((8?8)?5))?(7?(8?((((8?((((2?(8?(((3?6)?8)?7)))?5)?(8?(7?((4?(3?4))?(5?((1?(2?((2?(4?7))?(((6?1)?(4?(8?1)))?(1?(3?(((2?(2?(3?(8?9))))?(((((2?4)?7)?7)?(8?9))?7))?(((9?(7?3))?2)?((((((2?8)?6)?(1?3))?1)?7)?1)))))))))?(5?(6?(9?(5?4))))))))))?7))?5)?(8?(8?((5?7)?2))))?2))))?4)?(1?((7?4)?6)))?6))?6))
50 49
 (1?(2?2))
0 2
 (((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((3?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?2))?7)))))?4))?1)?7)
50 49
 ((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?5)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))
100 12
 (((6?((2?(9?(3?(2?((3?((1?(1?(6?(9?(((6?((3?(((((6?(1?(1?((((2?(1?(1?((6?(6?(4?(8?((9?(((7?((5?(9?(3?((((7?((9?(4?(8?(((((9?(1?(((8?(6?(6?((5?(((5?(7?((((1?((1?(4?((7?(8?(((3?((((3?((((((1?((3?((5?1)?9))?3))?9)?7)?7)?2)?8))?9)?1)?6))?9)?2)))?6)))?7))?4)?1)?1)))?6)?1))?9))))?8)?7)))?9)?3)?7)?7))))?1))?9)?6)?1))))?2))?2)?6))?6)))))?4))))?2)?3)?8))))?9)?1)?3)?1))?3))?9)?4)))))?1))?7)))))?4))?1)?7)
50 49
 ((1?(2?7))?((6?5)?6))
2 3
 ((7?(5?1))?((6?2)?7))
3 2
 (2?4)
1 0
 ((((4?6)?9)?((5?(7?1))?(6?(4?(((((((7?3)?7)?(((((8?(6?7))?((1?2)?(5?8)))?8)?7)?4))?6)?7)?1)?((7?(2?((1?(((8?(((((2?7)?(((((3?6)?3)?(((((9?4)?7)?(1?(5?5)))?(8?((3?(1?2))?((8?5)?(7?((9?((9?8)?7))?1))))))?1))?1)?(9?2)))?((7?5)?((9?(4?(9?6)))?(8?(((5?7)?2)?(6?(3?8)))))))?(((4?(2?2))?(7?9))?((7?((((4?(3?(7?3)))?8)?3)?(5?(((9?2)?(9?((((2?(7?3))?(3?(1?(9?(6?(9?8))))))?2)?2)))?2))))?((9?((2?(2?3))?((9?((7?4)?1))?5)))?((((9?6)?3)?(4?1))?7)))))?5))?4)?4))?7)))?5))))))?1)
2 114
 (1?(3?2))
0 2
 ((((4?6)?9)?((5?(7?1))?(6?(4?(((((((7?3)?7)?(((((8?(6?7))?((1?2)?(5?8)))?8)?7)?4))?6)?7)?1)?((7?(2?((1?(((8?(((((2?7)?(((((3?6)?3)?(((((9?4)?7)?(1?(5?5)))?(8?((3?(1?2))?((8?5)?(7?((9?((9?8)?7))?1))))))?1))?1)?(9?2)))?((7?5)?((9?(4?(9?6)))?(8?(((5?7)?2)?(6?(3?8)))))))?(((4?(2?2))?(7?9))?((7?((((4?(3?(7?3)))?8)?3)?(5?(((9?2)?(9?((((2?(7?3))?(3?(1?(9?(6?(9?8))))))?2)?2)))?2))))?((9?((2?(2?3))?((9?((7?4)?1))?5)))?((((9?6)?4)?(4?1))?7)))))?5))?4)?4))?7)))?5))))))?1)
2 114
 ((((3?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((6?(2?1))?6)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))
100 12
 (1?2)
1 0
 ((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?9)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(1?5))?(8?(3?((5?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?6)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))
100 12
 (2?1)
1 0
 (1?(1?2))
0 2
 (2?(3?2))
0 2
 (2?3)
1 0
 (2?(1?3))
0 2
 (3?2)
1 0
 ((((2?(2?((5?(((((((5?(5?6))?(((5?8)?(8?(2?2)))?(((8?(2?(((8?2)?3)?(4?8))))?(((((5?((3?1)?((3?8)?4)))?4)?5)?(6?2))?3))?(2?(((1?((((((9?1)?4)?7)?6)?(2?((((4?((((((1?8)?8)?(9?5))?(8?(3?((6?(5?2))?9))))?8)?5))?3)?(((5?(8?(2?(6?(6?(2?((4?(8?8))?(5?2))))))))?6)?3))?1)))?((9?(7?((7?(2?1))?5)))?4)))?((1?((((3?(5?(((2?6)?(7?((5?4)?(6?8))))?((2?(5?4))?9))))?((3?9)?7))?6)?8))?(2?9)))?6)))))?1)?4)?2)?(8?4))?(6?6)))?(2?((5?(9?8))?6)))))?9)?(4?4))?((7?2)?5))
100 12

18 2 16 1 422 8 85 423 86 550 11 439 549
 16
 438
 3
 2
 4
 423
 17
 5
 14
 19
 439
 1
 421
 548
 420
 15
 22
 6
 85
 0
 86
 549
 3
 549
 3
 2
 1
 5
 4
 5
 549
