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 $${\binom {n}{k}}$$ is divisible by pα.

As the answer can be rather large, print the remainder of the answer moduly 109 + 7.

Let us remind you that $${\binom {n}{k}}$$ is the number of ways k objects can be chosen from the set of n objects.

Input

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 < 101000) without leading zeroes.

Output

In the single line print the answer to the problem.

见题面 Input 部分

见题面 Output 部分

In the first sample three binominal coefficients divisible by 4 are $${ \binom { 4 } { 1 } } = 4$$, $${ \binom { 4 } { 3 } } = 4$$ and $${ \binom { 6 } { 3 } } = 20$$.