p02654 AtCoder Grand Contest 045 - Lamps and Buttons_5040
We have N lamps numbered 1 to N, and N buttons numbered 1 to N. Initially, Lamp 1, 2, \cdots, A are on, and the other lamps are off.

Snuke and Ringo will play the following game.

* First, Ringo generates a permutation (p_1,p_2,\cdots,p_N) of (1,2,\cdots,N). The permutation is chosen from all N! possible permutations with equal probability, without being informed to Snuke.

* Then, Snuke does the following operation any number of times he likes:

* Choose a lamp that is on at the moment. (The operation cannot be done if there is no such lamp.) Let Lamp i be the chosen lamp. Press Button i, which switches the state of Lamp p_i. That is, Lamp p_i will be turned off if it is on, and vice versa.



At every moment, Snuke knows which lamps are on. Snuke wins if all the lamps are on, and he will surrender when it turns out that he cannot win. What is the probability of winning when Snuke plays optimally?

Let w be the probability of winning. Then, w \times N! will be an integer. Compute w \times N! modulo (10^9+7).

Constraints

* 2 \leq N \leq 10^7
* 1 \leq A \leq \min(N-1,5000)

Input

Input is given from Standard Input in the following format:


N A


Output

Print w \times N! modulo (10^9+7), where w is the probability of Snuke's winning.

Examples

Input

3 1


Output

2


Input

3 2


Output

3


Input

8 4


Output

16776


Input

9999999 4999


Output

90395416
#include<bits/stdc++.h>
using namespace std;

#define int long long

#define rep(i,n) for(int i=0;i<(n);i++)
#define pb push_back
#define eb emplace_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second

using vint=vector<int>;
using pint=pair<int,int>;
using vpint=vector<pint>;

template<typename A,typename B>inline void chmin(A &a,B b){if(a>b)a=b;}
template<typename A,typename B>inline void chmax(A &a,B b){if(a<b)a=b;}

template<class A,class B>
ostream& operator<<(ostream& ost,const pair<A,B>&p){
	ost<<"{"<<p.first<<","<<p.second<<"}";
	return ost;
}

template<class T>
ostream& operator<<(ostream& ost,const vector<T>&v){
	ost<<"{";
	for(int i=0;i<v.size();i++){
		if(i)ost<<",";
		ost<<v[i];
	}
	ost<<"}";
	return ost;
}

inline int topbit(unsigned long long x){
	return x?63-__builtin_clzll(x):-1;
}

inline int popcount(unsigned long long x){
	return __builtin_popcountll(x);
}

inline int parity(unsigned long long x){
	return __builtin_parity(x);
}

template<uint32_t mod>
struct ModInt{
	uint32_t a;
	ModInt& s(uint32_t vv){
		a=vv<mod?vv:vv-mod;
		return *this;
	}

	ModInt(int64_t x=0){s(x%mod+mod);}

	ModInt& operator+=(const ModInt &x){return s(a+x.a);}
	ModInt& operator-=(const ModInt &x){return s(a+mod-x.a);}
	ModInt& operator*=(const ModInt &x){
		a=uint64_t(a)*x.a%mod;
		return *this;
	}
	ModInt& operator/=(const ModInt &x){
		*this*=x.inv();
		return *this;
	}

	ModInt operator+(const ModInt &x)const{return ModInt(*this)+=x;}
	ModInt operator-(const ModInt &x)const{return ModInt(*this)-=x;}
	ModInt operator*(const ModInt &x)const{return ModInt(*this)*=x;}
	ModInt operator/(const ModInt &x)const{return ModInt(*this)/=x;}
	bool operator==(const ModInt &x)const{return a==x.a;}
	bool operator!=(const ModInt &x)const{return a!=x.a;}
	bool operator<(const ModInt &x)const{return a<x.a;}

	ModInt operator-()const{return ModInt()-*this;}
	ModInt pow(int64_t n)const{
		ModInt res(1),x(*this);
		while(n){
			if(n&1)res*=x;
			x*=x;
			n>>=1;
		}
		return res;
	}

	ModInt inv()const{return pow(mod-2);}
};

template<uint32_t mod>
istream& operator>>(istream& in,ModInt<mod>& a){
	return (in>>a.a);
}
template<uint32_t mod>
ostream& operator<<(ostream& out,const ModInt<mod>& a){
	return (out<<a.a);
}
using mint=ModInt<1000000007>;

template<class Mint,int32_t lg>
struct ModIntTable{
	int N;
	vector<Mint>facts,finvs,invs;
	ModIntTable():N(1<<lg),facts(N),finvs(N),invs(N){
		const uint32_t mod=Mint(-1).a+1;
		invs[1]=1;
		for(int i=2;i<N;i++)invs[i]=invs[mod%i]*(mod-mod/i);

		facts[0]=1;
		finvs[0]=1;
		for(int i=1;i<N;i++){
			facts[i]=facts[i-1]*i;
			finvs[i]=finvs[i-1]*invs[i];
		}
	}
	inline Mint fact(int n)const{return facts[n];}
	inline Mint finv(int n)const{return finvs[n];}
	inline Mint inv(int n)const{return invs[n];}
	inline Mint binom(int n,int k)const{
		if(n<0||k<0||k>n)return 0;
		return facts[n]*finvs[k]*finvs[n-k];
	}
	inline Mint perm(int n,int k)const{
		if(n<0||k<0||k>n)return 0;
		return facts[n]*finvs[n-k];
	}
	inline Mint catalan(int n){
		return facts[2*n]*finvs[n+1]*finvs[n];
	}
};
ModIntTable<mint,24>mt;

signed main(){
	int N,A;
	cin>>N>>A;

	mint ans=0;
	for(int i=1;i<=A;i++){
		mint num=0;
		int r=max(0ll,A-i-1);

		for(int j=0;j<=i;j++){
			mint tmp=mt.fact(i-j)*mt.perm(i-j+(N-A)-1,N-A)*mt.binom(i,j);
			tmp*=mt.perm(i-j+N-A+r,r);
			if(j&1)num-=tmp;
			else num+=tmp;
		}
		ans+=num;
	}
	cout<<ans<<endl;
	return 0;
}
