/*

                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                    prayer
*/

// g++ -std=c++11 a.cpp
#include<iostream>
#include<vector>
#include<string>
#include<algorithm>	
#include<map>
#include<set>
#include<unordered_map>
#include<utility>
#include<cmath>
#include<random>
#include<cstring>
#include<queue>
#include<stack>
#include<bitset>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#include<typeinfo>
#define loop(i,a,b) for(long long i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define FOR(i,a) for(auto i:a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
#define show1d(v) rep(_,v.size())cout<<" "<<v[_];cout<<endl;
#define show2d(v) rep(__,v.size()){rep(_,v[__].size())cout<<" "<<v[__][_];cout<<endl;}
using namespace std;
//kaewasuretyuui
typedef long long ll;
#define int ll
typedef int Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
// #define mt make_tuple
// typedef tuple<int,int,int> tp;
// typedef vector<tp> vt;
template<typename A,typename B>bool cmin(A &a,const B &b){return a>b?(a=b,true):false;}
template<typename A,typename B>bool cmax(A &a,const B &b){return a<b?(a=b,true):false;}
//template<class C>constexpr int size(const C &c){return (int)c.size();}
//template<class T,size_t N> constexpr int size(const T (&xs)[N])noexcept{return (int)N;}
const double PI=acos(-1);
const double EPS=1e-9;
Def inf = sizeof(Def) == sizeof(long long) ? 2e18 : 1e9+10;
int dx[]={0,1,0,-1};
int dy[]={1,0,-1,0};

//nCr mod m
#define MOD 1000000007
#define M 1000000
vector<ll> fact;
bool h=false;
void init(){
	h=true;
	fact=vector<ll>(M);
	fact[0]=fact[1]=1;
	loop(i,2,M)fact[i]=fact[i-1]*i%MOD;
}
// a^b mod MOD
ll powmod(ll a,ll b,ll m=MOD){
	ll out=1;
	ll p=a%m;
	while(b){
		if(b&1)out=out*p%m;
		p=p*p%m;
		b>>=1;
	}
	return out;
}
signed main(){
	int n,k;
	cin>>n>>k;
	int out=0;
	vvi dp(n+1,vi(4000));
	dp[0][0]=1;
	rep(i,n)rep(j,4000)if(dp[i][j])rep(l,k+1){
		if(l<=n-i)(dp[i+1][j+(l+j)/(n-i)]+=dp[i][j])%=MOD;
		else (dp[i+1][j]+=dp[i][j])%=MOD;
	}
	
	rep(i,4000)(out+=dp[n][i]*i%MOD)%=MOD;
	(out=n*k*(k+1)/2%MOD*powmod(k+1,n-1)%MOD-out+MOD)%=MOD;
	cout<<out<<endl;
}















### Prompt

Please create a solution in Cpp to the following problem:

Consider the following game:

* The game is played using a row of N squares and many stones.
* First, a_i stones are put in Square i\ (1 \leq i \leq N).
* A player can perform the following operation as many time as desired: "Select an integer i such that Square i contains exactly i stones. Remove all the stones from Square i, and add one stone to each of the i-1 squares from Square 1 to Square i-1."
* The final score of the player is the total number of the stones remaining in the squares.



For a sequence a of length N, let f(a) be the minimum score that can be obtained when the game is played on a.

Find the sum of f(a) over all sequences a of length N where each element is between 0 and K (inclusive). Since it can be extremely large, find the answer modulo 1000000007 (= 10^9+7).

Constraints

* 1 \leq N \leq 100
* 1 \leq K \leq N

Input

Input is given from Standard Input in the following format:


N K


Output

Print the sum of f(a) modulo 1000000007 (= 10^9+7).

Examples

Input

2 2


Output

10


Input

20 17


Output

983853488

### Response

```cpp
/*

                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                    prayer
*/

// g++ -std=c++11 a.cpp
#include<iostream>
#include<vector>
#include<string>
#include<algorithm>	
#include<map>
#include<set>
#include<unordered_map>
#include<utility>
#include<cmath>
#include<random>
#include<cstring>
#include<queue>
#include<stack>
#include<bitset>
#include<cstdio>
#include<sstream>
#include<iomanip>
#include<assert.h>
#include<typeinfo>
#define loop(i,a,b) for(long long i=a;i<b;i++) 
#define rep(i,a) loop(i,0,a)
#define FOR(i,a) for(auto i:a)
#define pb push_back
#define all(in) in.begin(),in.end()
#define shosu(x) fixed<<setprecision(x)
#define show1d(v) rep(_,v.size())cout<<" "<<v[_];cout<<endl;
#define show2d(v) rep(__,v.size()){rep(_,v[__].size())cout<<" "<<v[__][_];cout<<endl;}
using namespace std;
//kaewasuretyuui
typedef long long ll;
#define int ll
typedef int Def;
typedef pair<Def,Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def,pii> pip;
typedef vector<pip>vip;
// #define mt make_tuple
// typedef tuple<int,int,int> tp;
// typedef vector<tp> vt;
template<typename A,typename B>bool cmin(A &a,const B &b){return a>b?(a=b,true):false;}
template<typename A,typename B>bool cmax(A &a,const B &b){return a<b?(a=b,true):false;}
//template<class C>constexpr int size(const C &c){return (int)c.size();}
//template<class T,size_t N> constexpr int size(const T (&xs)[N])noexcept{return (int)N;}
const double PI=acos(-1);
const double EPS=1e-9;
Def inf = sizeof(Def) == sizeof(long long) ? 2e18 : 1e9+10;
int dx[]={0,1,0,-1};
int dy[]={1,0,-1,0};

//nCr mod m
#define MOD 1000000007
#define M 1000000
vector<ll> fact;
bool h=false;
void init(){
	h=true;
	fact=vector<ll>(M);
	fact[0]=fact[1]=1;
	loop(i,2,M)fact[i]=fact[i-1]*i%MOD;
}
// a^b mod MOD
ll powmod(ll a,ll b,ll m=MOD){
	ll out=1;
	ll p=a%m;
	while(b){
		if(b&1)out=out*p%m;
		p=p*p%m;
		b>>=1;
	}
	return out;
}
signed main(){
	int n,k;
	cin>>n>>k;
	int out=0;
	vvi dp(n+1,vi(4000));
	dp[0][0]=1;
	rep(i,n)rep(j,4000)if(dp[i][j])rep(l,k+1){
		if(l<=n-i)(dp[i+1][j+(l+j)/(n-i)]+=dp[i][j])%=MOD;
		else (dp[i+1][j]+=dp[i][j])%=MOD;
	}
	
	rep(i,4000)(out+=dp[n][i]*i%MOD)%=MOD;
	(out=n*k*(k+1)/2%MOD*powmod(k+1,n-1)%MOD-out+MOD)%=MOD;
	cout<<out<<endl;
}















```