AT_abc438_g [ABC438G] Sum of Min

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 $ .

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

### Sample Explanation 1 The desired value is $ \min(3,1)+\min(1,5)+\min(4,1)+\min(3,5)+\min(1,1)=7 $ . ### Sample Explanation 3 Compute 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.