# Test Data Generation

## 题目描述

Test data generation is not an easy task! Often, generating big random test cases is not enough to ensure thorough testing of solutions for correctness. For example, consider a problem from an old Codeforces round. Its input format looks roughly as follows: The first line contains a single integer $n$ ( $1<=n<=max_{n}$ ) — the size of the set. The second line contains $n$ distinct integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=max_{a}$ ) — the elements of the set in increasing order. If you don't pay attention to the problem solution, it looks fairly easy to generate a good test case for this problem. Let $n=max_{n}$ , take random distinct $a_{i}$ from 1 to $max_{a}$ , sort them... Soon you understand that it's not that easy. Here is the actual problem solution. Let $g$ be the greatest common divisor of $a_{1},a_{2},...,a_{n}$ . Let $x=a_{n}/g-n$ . Then the correct solution outputs "Alice" if $x$ is odd, and "Bob" if $x$ is even. Consider two wrong solutions to this problem which differ from the correct one only in the formula for calculating $x$ . The first wrong solution calculates $x$ as $x=a_{n}/g$ (without subtracting $n$ ). The second wrong solution calculates $x$ as $x=a_{n}-n$ (without dividing by $g$ ). A test case is interesting if it makes both wrong solutions output an incorrect answer. Given $max_{n}$ , $max_{a}$ and $q$ , find the number of interesting test cases satisfying the constraints, and output it modulo $q$ .

## 输入输出格式

### 输入格式

The only line contains three integers $max_{n}$ , $max_{a}$ and $q$ ( $1<=max_{n}<=30000$ ; $max_{n}<=max_{a}<=10^{9}$ ; $10^{4}<=q<=10^{5}+129$ ).

### 输出格式

Output a single integer — the number of test cases which satisfy the constraints and make both wrong solutions output an incorrect answer, modulo $q$ .

## 输入输出样例

### 输入样例 #1

3 6 100000


### 输出样例 #1

4


### 输入样例 #2

6 21 100129


### 输出样例 #2

154


### 输入样例 #3

58 787788 50216


### 输出样例 #3

46009


## 说明

In the first example, interesting test cases look as follows: <br></br>1 1 1 3<br></br>2 4 6 2 4 6<br></br>