Height All the Same

题意翻译

### 题目描述 最近，Alice 迷上了一款名为 Sirtet 的游戏。 在 Sirtet 中，玩家会得到一个 $n \times m$ 的网格。初始时，格 $(i, j)$ 上码放有 $a_{i, j}$ 个方块。若两个格子有一条公共边，我们称这两个格子时相邻的。玩家可以进行以下两种操作： - 在两个相邻的格子上各码上一个方块。 - 在一个格子上码上两个方块。 上述中所提到的所有方块都具有相同的高度。 以下是该游戏的一个图例说明。图中右侧的状态是由图中左侧的状态经过一次上述操作得到，灰色的方块表示操作中新加入的方块。  玩家的目标是通过这些操作，使得所有的格子拥有同样的高度（也就是说，每个格子上堆放的方块数相同）。 然而，Alice 发现存在有某些初始局面，使得无论她采用什么策略，都无法达到目标。因此，她希望知道有多少初始局面，满足， - 对于所有的 $1 \le i \le n$，$1 \le j \le m$，$L \le a_{i, j} \le R$。 - 玩家可以通过执行这些操作，达到目标。 请帮助 Alice 解决这个问题。注意答案可能很大，请输出所求答案对 $998, 244, 353$ 取模的值。 ### 输入格式 输入一行四个整数 $n, m, L, R ~ (1 \le n, m, L, R \le 10 ^ 9; L \le R; n \cdot m \ge 2)$。 ### 输出格式 输出一个整数，表示所求答案对 $998, 244, 353$ 取模的值。 ### 说明/提示 在第一个样例中，唯一一种符合要求的初始局面是 $a_{1, 1} = a_{2, 1} = a_{1, 2} = a_{2, 2} = 1$。因此答案为 $1$。 在第二个样例中，符合要求的初始局面有 $a_{1, 1} = a_{1, 2} = 1$ 和 $a_{1, 1} = a_{1, 2} = 2$。因此答案为 $2$。

题目描述

Alice has got addicted to a game called Sirtet recently. In Sirtet, player is given an $ n \times m $ grid. Initially $ a_{i,j} $ cubes are stacked up in the cell $ (i,j) $ . Two cells are called adjacent if they share a side. Player can perform the following operations: - stack up one cube in two adjacent cells; - stack up two cubes in one cell. Cubes mentioned above are identical in height. Here is an illustration of the game. States on the right are obtained by performing one of the above operations on the state on the left, and grey cubes are added due to the operation. Player's goal is to make the height of all cells the same (i.e. so that each cell has the same number of cubes in it) using above operations. Alice, however, has found out that on some starting grids she may never reach the goal no matter what strategy she uses. Thus, she is wondering the number of initial grids such that - $ L \le a_{i,j} \le R $ for all $ 1 \le i \le n $ , $ 1 \le j \le m $ ; - player can reach the goal using above operations. Please help Alice with it. Notice that the answer might be large, please output the desired value modulo $ 998,244,353 $ .

输入输出格式

输入格式

The only line contains four integers $ n $ , $ m $ , $ L $ and $ R $ ( $ 1\le n,m,L,R \le 10^9 $ , $ L \le R $ , $ n \cdot m \ge 2 $ ).

输出格式

Output one integer, representing the desired answer modulo $ 998,244,353 $ .

输入输出样例

输入样例 #1

2 2 1 1

输出样例 #1

1

输入样例 #2

1 2 1 2

输出样例 #2

2

说明

In the first sample, the only initial grid that satisfies the requirements is $ a_{1,1}=a_{2,1}=a_{1,2}=a_{2,2}=1 $ . Thus the answer should be $ 1 $ . In the second sample, initial grids that satisfy the requirements are $ a_{1,1}=a_{1,2}=1 $ and $ a_{1,1}=a_{1,2}=2 $ . Thus the answer should be $ 2 $ .