2507: Number of Binominal Coefficients
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Description
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 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 
.