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#F1545. Number of Binominal Coefficients

    ID: 1551 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 10 上传者: 标签>动态规划数学数论挑战难度共享题库Codeforces英文题面题目来源题面语言

Number of Binominal Coefficients

题目描述

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 .

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 1064 题。保留原作者与原赛事署名。