Ascending Matrix

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문제

You are given integers N,M,K,R,C,N,M,K,R,C, and VV. Find the number of NN by MM integer matrices a=(a_i,j)a = (a\_{i,j}) that satisfy all of the following conditions, modulo 998244353998244353.

  • 1a_i,jK1 \leq a\_{i,j} \leq K for all 1iN,,1jM1 \leq i \leq N,\\, 1 \leq j \leq M.
  • a_i,ja_i,j+1a\_{i,j} \leq a\_{i,j+1} for all 1iN,,1jM11 \leq i \leq N,\\, 1 \leq j \leq M-1.
  • a_i,ja_i+1,ja\_{i,j} \leq a\_{i+1,j} for all 1iN1,,1jM1 \leq i \leq N-1,\\, 1 \leq j \leq M.
  • a_R,C=Va\_{R,C}=V.

입력

The first line contains integers NN, MM (1N,M2001 \leq N,M \leq 200), KK (1K1001 \leq K \leq 100), RR (1RN1 \leq R \leq N), CC (1CM1 \leq C \leq M), and VV (1VK1 \leq V \leq K).

출력

Print the answer.