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

  * the length of both arrays is equal to m; 
  * each element of each array is an integer between 1 and n (inclusive); 
  * a_i ≤ b_i for any index i from 1 to m; 
  * array a is sorted in non-descending order; 
  * array b is sorted in non-ascending order. 



As the result can be very large, you should print it modulo 10^9+7.

Input

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

Output

Print one integer – the number of arrays a and b satisfying the conditions described above modulo 10^9+7.

Examples

Input


2 2


Output


5


Input


10 1


Output


55


Input


723 9


Output


157557417

Note

In the first test there are 5 suitable arrays: 

  * a = [1, 1], b = [2, 2]; 
  * a = [1, 2], b = [2, 2]; 
  * a = [2, 2], b = [2, 2]; 
  * a = [1, 1], b = [2, 1]; 
  * a = [1, 1], b = [1, 1]. 
#include <bits/stdc++.h>
using namespace std;
long long fac[1020];
long long facInv[1020];
long long ways[1020];
long long waysminus1[1020];
long long modInv(long long val) {
  long long ret = 1;
  long long mult = val;
  long long k = 1000000007 - 2;
  while (k > 0) {
    if ((k & 1) > 0) ret = (ret * mult) % 1000000007;
    mult = (mult * mult) % 1000000007;
    k >>= 1;
  }
  return ret;
}
void fillfac(int maxVal) {
  fac[0] = 1;
  facInv[0] = 1;
  for (int i = 1; i <= maxVal; i++) {
    long long temp = fac[i - 1] * i;
    if (temp >= 1000000007) temp = temp % 1000000007;
    fac[i] = temp;
    facInv[i] = modInv(fac[i]);
  }
}
void fillWays(int maxVal, int m) {
  for (int i = 1; i <= maxVal; i++) {
    long long num = fac[i + m - 1];
    long long denom = facInv[m] * facInv[i - 1];
    if (denom >= 1000000007) denom = denom % 1000000007;
    ways[i] = num * denom;
    if (ways[i] >= 1000000007) ways[i] = ways[i] % 1000000007;
    num = fac[i + m - 2];
    denom = facInv[m - 1] * facInv[i - 1];
    if (denom >= 1000000007) denom = denom % 1000000007;
    waysminus1[i] = num * denom;
    if (waysminus1[i] >= 1000000007) waysminus1[i] = waysminus1[i] % 1000000007;
  }
}
int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  fillfac(n + m);
  fillWays(n, m);
  long long totalWays = 0;
  for (int divider = 1; divider <= n; divider++) {
    long long curWays = waysminus1[divider] * ways[n - divider + 1];
    if (curWays >= 1000000007) curWays = curWays % 1000000007;
    totalWays += curWays;
    if (totalWays >= 1000000007) totalWays = totalWays % 1000000007;
  }
  printf("%lld\n", totalWays);
}
