For a given prime integer p and integers α, A calculate the number of pairs of integers (n, k), such that 0 ≤ k ≤ n ≤ A and is divisible by p α . As the answer can be rather large, print the remainder of the answer moduly 109 + 7. Let us remind you that is the number of ways k objects can be chosen from the set of n objects.

输入描述:

The first line contains two integers, p and α (1 ≤ p, α ≤ 109, p is prime). The second line contains the decimal record of integer A (0 ≤ A 1000) without leading zeroes.

输出描述:

In the single line print the answer to the problem.

备注:

In the first sample three binominal coefficients divisible by 4 are , and .