5192: GukiZ and Binary Operations
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
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题目描述
D. GukiZ and Binary Operations
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
We all know that GukiZ often plays with arrays.
Now he is thinking about this problem: how many arrays a, of length n, with non-negative elements strictly less then 2l meet the following condition:
? Here operation 
means bitwise AND (in Pascal it is equivalent to and, in C/C++/Java/Python it is equivalent to &), operation 
means bitwise OR (in Pascal it is equivalent to , in C/C++/Java/Python it is equivalent to |).
Because the answer can be quite large, calculate it modulo m. This time GukiZ hasn't come up with solution, and needs you to help him!
Now he is thinking about this problem: how many arrays a, of length n, with non-negative elements strictly less then 2l meet the following condition:
? Here operation means bitwise AND (in Pascal it is equivalent to and, in C/C++/Java/Python it is equivalent to &), operation means bitwise OR (in Pascal it is equivalent to , in C/C++/Java/Python it is equivalent to |). Because the answer can be quite large, calculate it modulo m. This time GukiZ hasn't come up with solution, and needs you to help him!
Input
First and the only line of input contains four integers n, k, l, m (2≤n≤1018, 0≤k≤1018, 0≤l≤64, 1≤m≤109+7).
Output
In the single line print the number of arrays satisfying the condition above modulo m.
Examples
Input
2 1 2 10
Output
3
Input
2 1 1 3
Output
1
Input
3 3 2 10
Output
9
Note
In the first sample, satisfying arrays are {1,1},{3,1},{1,3}. In the second sample, only satisfying array is {1,1}.
In the third sample, satisfying arrays are {0,3,3},{1,3,2},{1,3,3},{2,3,1},{2,3,3},{3,3,0},{3,3,1},{3,3,2},{3,3,3}.
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