链接：https://codeforces.com/contest/1288/problem/C

You are given two integers nn and mm. Calculate the number of pairs of arrays (a,b)(a,b) such that:

  • the length of both arrays is equal to mm;
  • each element of each array is an integer between 11 and nn (inclusive);
  • ai≤biai≤bi for any index ii from 11 to mm;
  • array aa is sorted in non-descending order;
  • array bb is sorted in non-ascending order.

As the result can be very large, you should print it modulo 109+7109+7.

Input

The only line contains two integers nn and mm (1≤n≤10001≤n≤1000, 1≤m≤101≤m≤10).

Output

Print one integer – the number of arrays aa and bb satisfying the conditions described above modulo 109+7109+7.

Examples

input

Copy

2 2

output

Copy

5

input

Copy

10 1

output

Copy

55

input

Copy

723 9

output

Copy

157557417

Note

In the first test there are 55 suitable arrays:

  • a=[1,1],b=[2,2]a=[1,1],b=[2,2];
  • a=[1,2],b=[2,2]a=[1,2],b=[2,2];
  • a=[2,2],b=[2,2]a=[2,2],b=[2,2];
  • a=[1,1],b=[2,1]a=[1,1],b=[2,1];
  • a=[1,1],b=[1,1]a=[1,1],b=[1,1].

代码：

#include<bits/stdc++.h>
using namespace std;
long long n,m,t,k,x,d,max1=0,a,b,c,mod=1e9+7;
long long dp[2005][2005];
main()
{
	cin>>n>>m;
	dp[0][0]=1;
	for(int i=1;i<=2000;i++)
	{
		for(int j=0;j<=i;j++)
		{
			if(j>0)
			dp[i][j]=(dp[i][j]+dp[i-1][j-1])%mod;
			if(j<i)
			dp[i][j]=(dp[i][j]+dp[i-1][j])%mod;
		}
	}
	cout<<dp[n+2*m-1][2*m];
}