Problem Statement

You are given integers $N,M,K$, a length-$N$ integer sequence $A=(A_0,A_1,\ldots,A_{N-1})$, and a length-$M$ integer sequence $B=(B_0,B_1,\ldots,B_{M-1})$. Note that the indices start from $0$.

Find $\displaystyle\sum_{i=0}^{K-1} \min(A_{i\bmod N}, B_{i \bmod M})$, modulo $998244353$.

Constraints

• $1\le N,M\le 2\times 10^5$
• $1\le K\le 10^{18}$
• $1\le A_i,B_i\le 10^9$
• All input values are integers.

Input

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

N M K
A_0 A_1 \ldots A_{N-1}
B_0 B_1 \ldots B_{M-1}

Output

Output $\displaystyle\sum_{i=0}^{K-1} \min(A_{i\bmod N}, B_{i \bmod M})$, modulo $998244353$.