Codeforces Round 323 (Div. 1) |
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Finished |

dp

math

number theory

*3300

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D. Number of Binominal Coefficients

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFor 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 *p*^{α}.

As the answer can be rather large, print the remainder of the answer moduly 10^{9} + 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 ≤ 10^{9}, *p* is prime).

The second line contains the decimal record of integer *A* (0 ≤ *A* < 10^{1000}) 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 .

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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