D. Number of Binominal Coefficients
time limit per test
4 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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 pα.

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.

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.

Examples
Input
2 2
7
Output
3
Input
3 1
9
Output
17
Input
3 3
9
Output
0
Input
2 4
5000
Output
8576851
Note

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