The Maths Lecture

1000ms

262144K

Description:

Amr doesn't like Maths as he finds it really boring, so he usually sleeps in Maths lectures. But one day the teacher suspected that Amr is sleeping and asked him a question to make sure he wasn't.

First he gave Amr two positive integers n and k. Then he asked Amr, how many integer numbers x > 0 exist such that:

Decimal representation of x (without leading zeroes) consists of exactly n digits;
There exists some integer y > 0 such that:
- $\text{[math]}$ ;
- decimal representation of y is a suffix of decimal representation of x.

As the answer to this question may be pretty huge the teacher asked Amr to output only its remainder modulo a number m.

Can you help Amr escape this embarrassing situation?

Input:

Input consists of three integers n, k, m (1 ≤ n ≤ 1000, 1 ≤ k ≤ 100, 1 ≤ m ≤ 10⁹).

Output:

Print the required number modulo m.

Sample Input:

1 2 1000

Sample Output:

Sample Input:

2 2 1000

Sample Output:

Sample Input:

5 3 1103

Sample Output:

Note:

A suffix of a string S is a non-empty string that can be obtained by removing some number (possibly, zero) of first characters from S.

Informação

Provedor Codeforces

Código CF507D