AT_arc192_e [ARC192E] Snuke's Kyoto Trip

You are given integers $ W,H,L,R,D,U $ . A town of Kyoto is on the two-dimensional plane. In the town, there is exactly one block at each lattice point $ (x,y) $ that satisfies all of the following conditions. There are no blocks at any other points. - $ 0\leq x\leq W $ - $ 0\leq y\leq H $ - $ x

The input is given from Standard Input in the following format: > $ W $ $ H $ $ L $ $ R $ $ D $ $ U $

Print the answer.

### Sample Explanation 1 The following are examples of possible paths. Here, a path is represented by listing the lattice points visited in order. - $ (3,0) $ - $ (0,0)\rightarrow (1,0)\rightarrow (2,0)\rightarrow (2,1)\rightarrow (3,1)\rightarrow (3,2)\rightarrow (4,2)\rightarrow (4,3) $ - $ (0,1)\rightarrow (0,2) $ There are $ 192 $ possible paths. ### Sample Explanation 3 Do not forget to print the number of paths modulo $ 998244353 $ . ### Constraints - $ 0\leq L\leq R\leq W\leq 10^6 $ - $ 0\leq D\leq U\leq H\leq 10^6 $ - There is at least one block. - All input values are integers.