Problem Statement

You are given positive integers $N$, $M$, and $K$. Consider the following operation on a sequence of positive integers $A = (A_0, \ldots, A_{N-1})$.

• Do the following for $k=0, 1, \ldots, K-1$ in this order.
• Sort $A_{k\bmod N}, A_{(k+1)\bmod N}, \ldots, A_{(k+M-1)\bmod N}$ in ascending order. That is, replace $A_{(k+j)\bmod N}$ with $x_j$ for each $0\leq j < M$, where $(x_0, \ldots, x_{M-1})$ is the result of sorting $A_{k\bmod N}, A_{(k+1)\bmod N}, \ldots, A_{(k+M-1)\bmod N}$ in ascending order.

You are given a permutation $B = (B_0, \ldots, B_{N-1})$ of the integers from $1$ through $N$. Find the number of sequences $A$ of positive integers that will equal $B$ after performing the operation above, modulo $998244353$.

Constraints

• $2\leq N\leq 3\times 10^5$
• $2\leq M\leq N$
• $1\leq K\leq 10^9$
• $1\leq B_i\leq N$
• $B_i\neq B_j$ if $i\neq j$.

Input

The input is given from Standard Input in the following format:

N M K
B_0 \ldots B_{N-1}

Print

Print the number of sequences $A$ of positive integers that will equal $B$ after performing the operation, modulo $998244353$.