Problem: 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

Solution (in CPP):

Solution:
#include "bits/stdc++.h"
#include <random>
using namespace std;
using ll    =long long;    using dd   =double;        using pll    =pair<ll, ll>;  using tll    =tuple<ll,ll,ll>;
using vll   =vector<ll>;   using vdd  =vector<dd>;    using vpll   =vector<pll>;   using vtll   =vector<tll>;
using vvll  =vector<vll>;  using vvdd =vector<vdd>;   using vvpll  =vector<vpll>;  using vvtll  =vector<vtll>;
using vvvll =vector<vvll>; using vvvdd=vector<vvdd>;  using vvvpll =vector<vvpll>; using vvvtll =vector<vvtll>;
using vvvvll=vector<vvvll>;using vvvvdd=vector<vvvdd>;using vvvvpll=vector<vvvpll>;using vvvvtll=vector<vvvtll>;

constexpr ll INF = 1LL << 60;
constexpr dd EPS = 1e-11;
constexpr dd PI  = 3.1415926535897932;

//cin,cout高速化のおまじない＋桁数指定
struct Fast{
	Fast(){
		cin.tie(0);
		ios::sync_with_stdio(false);
		cout << fixed << setprecision(std::numeric_limits<double>::max_digits10);
	}
} fast;

#define REPS(i, S, E) for (ll i = (S); i <= (E); i++)
#define rep(i, S, E)  for (ll i = (S); i <= (E); i++)
#define REP(i, N) REPS(i, 0, (N)-1)
#define DEPS(i, S, E) for (ll i = (E); i >= (S); i--)
#define dep(i, E, S)  for (ll i = (E); i >= (S); i--)
#define DEP(i, N) DEPS(i, 0, (N)-1)
#define EACH(e, v) for (auto&& e : v)
#define each(e, v) for (auto&& e : v)
#define ALL(v) (v).begin(), (v).end()
#define RALL(v) (v).rbegin(), (v).rend()

template<class T> inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; }return false; }
template<class T> inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; }return false; }
template<class T> inline T MaxE(vector<T>&v,ll S,ll E){T m=v[S]; REPS(i,S,E)chmax(m,v[i]); return m;}//v[S]～v[E]の最大値
template<class T> inline T MinE(vector<T>&v,ll S,ll E){T m=v[S]; REPS(i,S,E)chmin(m,v[i]); return m;}//v[S]～v[E]の最小値
template<class T> inline T MaxE(vector<T> &v, ll N) { return MaxE(v, 0, N - 1); } //先頭N個中の最大値
template<class T> inline T MinE(vector<T> &v, ll N) { return MinE(v, 0, N - 1); }
template<class T> inline T MaxE(vector<T> &v) { return MaxE(v, (ll)v.size()); }
template<class T> inline T MinE(vector<T> &v) { return MinE(v, (ll)v.size()); }
template<class T> inline ll MaxI(vector<T>&v,ll S,ll E){ll m=S; REPS(i,S,E){if(v[i]>v[m])m=i;} return m;}
template<class T> inline ll MinI(vector<T>&v,ll S,ll E){ll m=S; REPS(i,S,E){if(v[i]<v[m])m=i;} return m;}
template<class T> inline ll MaxI(vector<T> &v, ll N) { return MaxI(v, 0, N - 1); }
template<class T> inline ll MinI(vector<T> &v, ll N) { return MinI(v, 0, N - 1); }
template<class T> inline ll MaxI(vector<T> &v) { return MaxI(v, (ll)v.size()); }
template<class T> inline ll MinI(vector<T> &v) { return MinI(v, (ll)v.size()); }
template<class T> inline T Sum(vector<T> &v, ll S,ll E){ T s=v[S]; REPS(i,S+1,E)s+=v[i]; return s; }
template<class T> inline T Sum(vector<T> &v, ll N) { return Sum(v, 0, N - 1); }
template<class T> inline T Sum(vector<T> &v) { return Sum(v, v.size()); }
template<class T> inline ll sz(T &v){ return (ll)v.size(); }
template<class T> inline T POW(T a, ll n){ T r=1; for (; n>0; n>>=1, a*=a){ if (n&1)r*=a; } return r; }
inline ll POW(int a, ll n){ return POW((ll)a, n); }
inline ll CEIL(ll a, ll b){ return (a+b-1)/b; }
ll Gcd(ll a, ll b){ return (b==0) ? a : Gcd(b, a%b); }
ll Lcm(ll a, ll b){ return a * b / Gcd(a, b); }
inline ll MSB(ll a){for(ll o=63,x=-1;;){ll m=(o+x)/2; if(a<(1LL<<m))o=m; else x=m; if(o-x==1)return x;}}
inline ll Upper2N(ll s) { return 1LL<<MSB(s)<<1; }//s<2^nなる最小の2^n
inline vll Bit2Idx(ll m){vll v; for(ll i=0;m;m>>=1,i++) if(m&1)v.push_back(i); return move(v);}
inline ll BitNum(ll m){ for (ll c=0;; m>>=1){ c+=m&1; if (!m)return c; } }
inline ll Bit(ll s, ll i){ return (s>>i)&1; } //sの第ibit i=0-63
[[nodiscard]] inline ll BitOn(ll s, ll i){ return s|(1LL<<i); } //sの第ibitON i=0-63
[[nodiscard]] inline ll BitOff(ll s, ll i){ return s&~(1LL<<i); } //sの第ibitOFF i=0-63
[[nodiscard]] inline ll BitCut(ll s, ll i){ return s & (1LL<<++i)-1; }//sの第0～第ibitを抽出
inline vll str2num(string &s, ll N) {vll v(N); REP(i, N) v[i]=(ll)(s[i]-'0'); return move(v);}
inline vll ALP2num(string &s, ll N) {vll v(N); REP(i, N) v[i]=(ll)(s[i]-'A'); return move(v);}
inline vll alp2num(string &s, ll N) {vll v(N); REP(i, N) v[i]=(ll)(s[i]-'a'); return move(v);}
template<class T> inline ll FloorIdx(vector<T> &v, T x){ return upper_bound(ALL(v), x)-v.begin()-1; }
template<class T> inline ll CeilIdx(vector<T> &v, T x){ return lower_bound(ALL(v), x)-v.begin(); }
template<class T> inline ll UnderNumOf(vector<T> &v, T x){ //sort済vのx以下の個数を得る
	return upper_bound(v.begin(), v.end(), x) - v.begin(); }
template<class T, class Pr> inline ll UnderNumOf(vector<T> &v, T x, Pr pred){ //x以下個数
	return upper_bound(v.begin(), v.end(), x, pred) - v.begin(); }
template<class T> inline ll OverNumOf(vector<T> &v, T x){ //sort済vのx以上の個数を得る
	return (ll)v.size() - (lower_bound(v.begin(), v.end(), x) - v.begin()); }
template<class T, class Pr> inline ll OverNumOf(vector<T> &v, T x, Pr pred){ //x以上の個数
	return (ll)v.size() - (lower_bound(v.begin(), v.end(), x, pred) - v.begin()); }

template<class T=ll> inline vector<T> cinv(ll N){ vector<T> v(N); REP(i, N)cin>>v[i]; return move(v);}
template<class T=ll, class S=ll> inline vector<pair<T, S>> cinv2(ll N){
	vector<pair<T, S>> v(N); REP(i,N){cin>>v[i].first>>v[i].second;} return move(v); }
template<class T=ll,class S=ll,class R=ll> inline vector<tuple<T, S, R>> cinv3(ll N){
	vector<tuple<T,S,R>> v(N); REP(i,N){cin>>get<0>(v[i])>>get<1>(v[i])>>get<2>(v[i]);} return move(v);}
template<class T=ll,class S=ll,class R=ll,class Q=ll> inline vector<tuple<T,S,R,Q>> cinv4(ll N){
	vector<tuple<T,S,R,Q>> v(N); REP(i,N){cin>>get<0>(v[i])>>get<1>(v[i])>>get<2>(v[i])>>get<3>(v[i]);} return move(v);}
template<class T=ll> inline vector<vector<T>> cinvv(ll N, ll M){
	vector<vector<T>> vv(N); REP(i, N) vv[i] = cinv(M); return move(vv);}
template<class T> inline void coutv(vector<T> &v, string d=" "){
	ll N=(ll)v.size(); REP(i,N){cout << v[i] << ((i==N-1)?"":d);} cout<<'\n';}
template<class T> inline void coutv(deque<T> &v, string d=" "){
	ll N=(ll)v.size(); REP(i,N){cout << v[i] << ((i==N-1)?"":d);} cout<<'\n';}
template<class T> void bye(T a){cout << a << '\n'; exit(0);}

#if defined(_DEBUG)
ll dumpW = 5;
template<class T> void Dump(vector<T> &v){
	REP(i, (ll)v.size()) { cerr << ((i==0)?"[":" ") << setw(dumpW) << v[i]; }  cerr << "]";
}
void Dump(vll &v){
	REP(i, (ll)v.size()) {
		cerr << ((i==0)?"[":" ") << setw(dumpW);
		if       (v[i] == INF) cerr << "INF";
		else if (v[i] == -INF) cerr << "-INF";
		else                   cerr << v[i];
	}  cerr << "]";
}
template<class T> void Dump(vector<vector<T>> &v){
	ll N=(ll)v.size();  string d[2][2]={{" ", "["},  {"\n", "]\n"}};
	REP(i, N) { cerr << d[0][i==0];  Dump(v[i]);  cerr << d[1][i==N-1]; }
}
template<class T> void Dump(vector<vector<vector<T>>> &v){
	ll N=(ll)v.size();  string d[2]={"  <", "[ <"};
	REP(i, N) { cerr << d[i==0] << i << ">\n"; Dump(v[i]); }  cerr << "]\n";
}
template<class T> void Dump(vector<vector<vector<vector<T>>>> &v){
	ll N=(ll)v.size();  string d[2]={"  ---<", "[ ---<"};
	REP(i, N) { cerr << d[i==0] << i << ">---\n"; Dump(v[i]); }  cerr << "]\n";
}
template<class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v){
	ll N=(ll)v.size();  string d[2]={"  ======<", "[ ======<"};
	REP(i, N) { cerr << d[i==0] << i << ">======\n"; Dump(v[i]); }  cerr << "]\n";
}
template<class T, class S> void Dump(map<T, S> &m){
	for(auto e: m) cout << e.first << " : " << e.second << '\n';
}
#else
template<class T> void Dump(vector<T> &v){}
template<class T> void Dump(vector<vector<T>> &v){}
template<class T> void Dump(vector<vector<vector<T>>> &v){}
template<class T> void Dump(vector<vector<vector<vector<T>>>> &v){}
template<class T> void Dump(vector<vector<vector<vector<vector<T>>>>> &v){}
#endif

template<ll MOD> struct mll_{
	ll val;
	mll_(ll v = 0): val(v % MOD){ if (val < 0) val += MOD; }
	mll_ operator - () const { return -val; }
	mll_ operator + (const mll_ &b) const { return val + b.val; }
	mll_ operator - (const mll_ &b) const { return val - b.val; }
	mll_ operator * (const mll_ &b) const { return val * b.val; }
	mll_ operator / (const mll_ &b) const { return mll_(*this) /= b; }
	mll_ operator + (ll b) const { return *this + mll_(b); }
	mll_ operator - (ll b) const { return *this - mll_(b); }
	mll_ operator * (ll b) const { return *this * mll_(b); }
	friend mll_ operator + (ll a, const mll_ &b) { return b + a; }
	friend mll_ operator - (ll a, const mll_ &b) { return -b + a; }
	friend mll_ operator * (ll a, const mll_ &b) { return b * a; }
	friend mll_ operator / (ll a, const mll_ &b) { return mll_(a)/b; }
	mll_ &operator += (const mll_ &b) { val=(val+b.val)%MOD; return *this; }
	mll_ &operator -= (const mll_ &b) { val=(val+MOD-b.val)%MOD; return *this; }
	mll_ &operator *= (const mll_ &b) { val=(val*b.val)%MOD; return *this; }
	mll_ &operator /= (const mll_ &b) {
		ll c=b.val, d=MOD, u=1, v=0;
		while (d){
			ll t = c / d;
			c -= t * d; swap(c, d);
			u -= t * v; swap(u, v);
		}
		val = val * u % MOD;
		if (val < 0) val += MOD;
		return *this;
	}
	mll_ &operator += (ll b) { return *this += mll_(b); }
	mll_ &operator -= (ll b) { return *this -= mll_(b); }
	mll_ &operator *= (ll b) { return *this *= mll_(b); }
	mll_ &operator /= (ll b) { return *this /= mll_(b); }
	bool operator == (const mll_ &b) { return val == b.val; }
	bool operator != (const mll_ &b) { return val != b.val; }
	bool operator == (ll b) { return *this == mll_(b); }
	bool operator != (ll b) { return *this != mll_(b); }
	friend bool operator == (ll a, const mll_ &b) { return mll_(a) == b.val; }
	friend bool operator != (ll a, const mll_ &b) { return mll_(a) != b.val; }
	friend ostream &operator << (ostream &os, const mll_ &a) { return os << a.val; }
	friend istream &operator >> (istream &is, mll_ &a) { return is >> a.val; }
	static mll_ Combination(ll a, ll b){
		chmin(b, a-b);
		if (b<0) return mll_(0);
		mll_ c = 1;
		REP(i, b) c *= a-i;
		REP(i, b) c /= i+1;
		return c;
	}
};
using mll = mll_<1000000007LL>; //1000000007LL;// 998244353LL;
using vmll = std::vector<mll>;
using vvmll = std::vector<vmll>;
using vvvmll = std::vector<vvmll>;
using vvvvmll = std::vector<vvvmll>;
using vvvvvmll = std::vector<vvvvmll>;


struct Combination{
	vmll f, g; // factorial, factorial^-1
	Combination(){}
	Combination(ll maxN): f(maxN+1, 1), g(maxN+1){ InitSub(maxN); }
	void Init(ll maxN){ f.resize(maxN+1, 1); g.resize(maxN+1); InitSub(maxN); }
	mll operator () (ll n, ll r){ return (n<0||r<0||n<r) ? mll(0) : f[n]*g[n-r]*g[r]; }
	mll P(ll n, ll r){ return (n<0 || r<0 || n<r) ? mll(0) : f[n]*g[n-r]; }
	mll Inv(ll n) { return f[n-1] * g[n]; }
	mll Fact(ll n) { return f[n]; }
	mll FInv(ll n) { return g[n]; }
	void InitSub(ll maxN){
		REPS(i, 1, maxN){ f[i] = f[i-1] * i; }
		g[maxN] = 1 / f[maxN];
		DEPS(i, 1, maxN){ g[i-1] = g[i] * i; }
	}
};


void solve()
{
	ll n, a;  cin >> n >> a;
	ll b=n-a;
	Combination cmb(n+10);

	vvmll dp(a+1, vmll(a+1));
	auto Dp = [&](ll i, ll j)->mll&{
		static mll zero=0;
		if (j<0) return zero;
		return dp[i][j];
	};

	Dp(0, 0)=1;
#if 0
	rep(i, 1, a){
		rep(j, 0, a){
			rep(k, 0, i-2){
				Dp(i, j)+=Dp(k, j)*cmb.P(a-k-1, i-k-1);
			}
			Dp(i, j) += Dp(i-1, j-1);
		}
	}
#endif
	Dp(1, 1)=1;
	rep(i, 2, a){
		rep(j, 0, a){
			Dp(i,j) = ( Dp(i-1,j)-Dp(i-2,j-1)+Dp(i-2,j) )*(a-i+1)  + Dp(i-1,j-1);
		}
	}

	mll sum1=0;
	rep(j, 0, a){
		sum1 += cmb(b-j+a-1, a-1)*Dp(a, j)*cmb.Fact(b);
	}
	mll sum2=0;
	rep(i, 1, a-1)rep(j, 0, a){
		sum2 += cmb(b-j+i-1, i-1) * Dp(i, j) * cmb.Fact(a-i-1) * cmb.Fact(b);
	}

	mll ans=sum1+sum2;
	cout << ans << '\n';
}

int main(){
#if 1
	solve();
#else
	ll t;  cin >> t;
	rep(i, 0, t-1){
		solve();
	}
#endif
	return 0;
}