Number of Binominal Coefficients

4000ms

262144K

Description:

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 $\text{[math]}$ 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 $\text{[math]}$ 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.

Sample Input:

2 2
7

Sample Output:

Sample Input:

3 1
9

Sample Output:

Sample Input:

3 3
9

Sample Output:

Sample Input:

2 4
5000

Sample Output:

Note:

In the first sample three binominal coefficients divisible by 4 are $\text{[math]}$ , $\text{[math]}$ and $\text{[math]}$ .

Informação

Provedor Codeforces

Código CF582D