Codeforces Round 307 (Div. 2) |
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Finished |

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combinatorics

implementation

math

matrices

number theory

*2100

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D. GukiZ and Binary Operations

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWe 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 2^{l} 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* ≤ 10^{18}, 0 ≤ *k* ≤ 10^{18}, 0 ≤ *l* ≤ 64, 1 ≤ *m* ≤ 10^{9} + 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}.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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