Dreamoon Likes Sequences
Dreamoon likes sequences very much. So he created a problem about the sequence that you can't find in OEIS: You are given two integers $$$d, m$$$, find the number of arrays $$$a$$$, satisfying the following constraints:  The length of $$$a$$$ is $$$n$$$, $$$n \ge 1$$$  $$$1 \le a_1 < a_2 < \dots < a_n \le d$$$  Define an array $$$b$$$ of length $$$n$$$ as follows: $$$b_1 = a_1$$$, $$$\forall i > 1, b_i = b_{i - 1} \oplus a_i$$$, where $$$\oplus$$$ is the bitwise exclusive-or (xor). After constructing an array $$$b$$$, the constraint $$$b_1 < b_2 < \dots < b_{n - 1} < b_n$$$ should hold. Since the number of possible arrays may be too large, you need to find the answer modulo $$$m$$$.
The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 100$$$) denoting the number of test cases in the input.Each of the next $$$t$$$ lines contains two integers $$$d, m$$$ ($$$1 \leq d, m \leq 10^9$$$).Note that $$$m$$$ is not necessary the prime!
For each test case, print the number of arrays $$$a$$$, satisfying all given constrains, modulo $$$m$$$.
for q in range(int(input())):
    (n, m) = map(int, input().split())
    (st, ans) = (1, 1)
    while st <= n:
        ans *= min(st * 2 - st + 1, n - st + 2)
        st *= 2
    print((ans - 1) % m)
for _ in range(int(input())):
    [n, m] = list(map(int, input().split()))
    k = 1
    arr = []
    while n >= k:
        n -= k
        arr.append(k)
        k *= 2
    if n:
        arr.append(n)
    ans = 1
    for i in arr:
        ans *= i + 1
    print((ans - 1) % m)
for q in range(int(input())):
    (n, m) = map(int, input().split())
    (st, ans) = (1, 1)
    while st <= n:
        ans *= min(st * 2 - st + 1, n - st + 2)
        st *= 2
    print((ans - 1) % m)