Problem2386--GukiZ and Binary Operations

2386: GukiZ and Binary Operations

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

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!

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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