Score : $2000$ points

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 $D$.

2 2 2 998244353

35

We have $1$ way to write integers such that the product of the $NM$ values is $16$, $4$ ways such that the product is $2$, and $11$ ways such that the product is $1$.

2 3 4 998244353

127090

31 41 59 998244353

827794103