#D3015. Number of Binominal Coefficients
Number of Binominal Coefficients
Number of Binominal Coefficients
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 .
inputFormat
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.
outputFormat
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 .
样例
2 4
5000
8576851