Team Players

题意翻译

有 $n$ 个点，编号依次为 $0,1....n-1$。 如果一个三元组 $(i,j,k)~(i<j<k)$ 两两**没有边**相连，那么它的贡献为 $A*i+B*j+C*k$。 求出所有三元组的贡献和，答案对 $2^{64}$ 取模。

题目描述

There are $ n $ players numbered from $ 0 $ to $ n-1 $ with ranks. The $ i $ -th player has rank $ i $ . Players can form teams: the team should consist of three players and no pair of players in the team should have a conflict. The rank of the team is calculated using the following algorithm: let $ i $ , $ j $ , $ k $ be the ranks of players in the team and $ i < j < k $ , then the rank of the team is equal to $ A \cdot i + B \cdot j + C \cdot k $ . You are given information about the pairs of players who have a conflict. Calculate the total sum of ranks over all possible valid teams modulo $ 2^{64} $ .

输入输出格式

输入格式

The first line contains two space-separated integers $ n $ and $ m $ ( $ 3 \le n \le 2 \cdot 10^5 $ , $ 0 \le m \le 2 \cdot 10^5 $ ) — the number of players and the number of conflicting pairs. The second line contains three space-separated integers $ A $ , $ B $ and $ C $ ( $ 1 \le A, B, C \le 10^6 $ ) — coefficients for team rank calculation. Each of the next $ m $ lines contains two space-separated integers $ u_i $ and $ v_i $ ( $ 0 \le u_i, v_i < n, u_i \neq v_i $ ) — pair of conflicting players. It's guaranteed that each unordered pair of players appears in the input file no more than once.

输出格式

Print single integer — the total sum of ranks over all possible teams modulo $ 2^{64} $ .

输入输出样例

输入样例 #1

4 0
2 3 4

输出样例 #1

64

输入样例 #2

4 1
2 3 4
1 0

输出样例 #2

38

输入样例 #3

6 4
1 5 3
0 3
3 5
5 4
4 3

输出样例 #3

164

说明

In the first example all $ 4 $ teams are valid, i.e. triples: {0, 1, 2}, {0, 1, 3}, {0, 2, 3} {1, 2, 3}. In the second example teams are following: {0, 2, 3}, {1, 2, 3}. In the third example teams are following: {0, 1, 2}, {0, 1, 4}, {0, 1, 5}, {0, 2, 4}, {0, 2, 5}, {1, 2, 3}, {1, 2, 4}, {1, 2, 5}.