The Maths Lecture

题意翻译

输入三个数 $n,k,m$，有多少个 $n$ 位数有后缀可以被 $k$ 整除，答案对 $m$ 取模。

题目描述

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: - ; - 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?

输入输出格式

输入格式

Input consists of three integers $ n,k,m $ ( $ 1<=n<=1000 $ , $ 1<=k<=100 $ , $ 1<=m<=10^{9} $ ).

输出格式

Print the required number modulo $ m $ .

输入输出样例

输入样例 #1

1 2 1000

输出样例 #1

4

输入样例 #2

2 2 1000

输出样例 #2

45

输入样例 #3

5 3 1103

输出样例 #3

590

说明

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 $ .