Problem Statement

For each of the $K^{NM}$ ways to write an integer between $1$ and $K$ (inclusive) in every square in a square grid with $N$ rows and $M$ columns, find the value defined below, then compute the sum of all those $K^{NM}$ values, modulo $D$.

• For each of the $NM$ squares, find the minimum among the $N+M-1$ integers written in the square's row or the square's column. The value defined for the grid is the product of all these $NM$ values.

Constraints

• $1 \leq N,M,K \leq 100$
• $10^8 \leq D \leq 10^9$
• $N,M,K,$ and $D$ are integers.
• $D$ is prime.

Input

Input is given from Standard Input in the following format:

N M K D

Output

Print the sum of the $K^{NM}$ values, modulo $D$.