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]. 
def main():
    n, m = map(int, input().split())
    n, m, o, acc = n + 2 * m - 1, 2 * m, n - 1, [1] * 32
    for p in (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
              59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113,
              127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181,
              191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251,
              257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
              331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397,
              401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463,
              467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557,
              563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619,
              631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
              709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787,
              797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863,
              877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953,
              967, 971, 977, 983, 991, 997,1009, 1013, 1019):
        a, b, c, pw = n // p, m, o, 0
        while a:
            b //= p
            c //= p
            pw += a - b - c
            a //= p
        if pw:
            acc[pw] *= p
    res = acc.pop(1)
    for pw, pq in enumerate(acc, 1):
        if pq != 1:
            res = res * pow(pq, pw, 1000000007) % 1000000007
    print(res)


if __name__ == '__main__':
    main()
