CF901C.Bipartite Segments

You are given an undirected graph with n vertices. There are no edge-simple cycles with the even length in it. In other words, there are no cycles of even length that pass each edge at most once. Let's enumerate vertices from 1 to n.

You have to answer q queries. Each query is described by a segment of vertices [l; r], and you have to count the number of its subsegments [x; y] (l ≤ x ≤ y ≤ r), such that if we delete all vertices except the segment of vertices [x; y] (including x and y) and edges between them, the resulting graph is bipartite.

给你一个包含 $n$ 个顶点的无向图。该图中不存在长度为偶数的边简单环（即：不存在长度为偶数、且每条边至多经过一次的环）。我们对顶点从 $1$ 到 $n$ 编号。

你需要回答 $q$ 个查询。每个查询由一个顶点区间 $[l,\,r]$ 描述，你需要统计其子区间 $[x,\,y]$（满足 $l \le x \le y \le r$）的个数，使得：若仅保留顶点区间 $[x,\,y]$（含端点 $x$ 和 $y$）内的所有顶点及它们之间的边，则所得子图是二分图。

The first line contains two integers n and m (1 ≤ n ≤ 3·105, 1 ≤ m ≤ 3·105) — the number of vertices and the number of edges in the graph.

The next m lines describe edges in the graph. The i-th of these lines contains two integers a__i and b__i (1 ≤ a__i, b__i ≤ n; a__i ≠ b__i), denoting an edge between vertices a__i and b__i. It is guaranteed that this graph does not contain edge-simple cycles of even length.

The next line contains a single integer q (1 ≤ q ≤ 3·105) — the number of queries.

The next q lines contain queries. The i-th of these lines contains two integers l__i and r__i (1 ≤ l__i ≤ r__i ≤ n) — the query parameters.

第一行包含两个整数 $n$ 和 $m$（$1 ≤ n ≤ 3·10^5$，$1 ≤ m ≤ 3·10^5$）—— 分别表示图中的顶点数和边数。

接下来的 $m$ 行描述图中的边。其中第 $i$ 行包含两个整数 $a_i$ 和 $b_i$（$1 ≤ a_i,\,b_i ≤ n$；$a_i ≠ b_i$），表示顶点 $a_i$ 与 $b_i$ 之间存在一条边。保证该图不包含长度为偶数的边简单环。

下一行包含一个整数 $q$（$1 ≤ q ≤ 3·10^5$）—— 表示查询的数量。

接下来的 $q$ 行包含查询。其中第 $i$ 行包含两个整数 $l_i$ 和 $r_i$（$1 ≤ l_i ≤ r_i ≤ n$）—— 表示第 $i$ 个查询的参数。

Print q numbers, each in new line: the i-th of them should be the number of subsegments [x; y] (l__i ≤ x ≤ y ≤ r__i), such that the graph that only includes vertices from segment [x; y] and edges between them is bipartite.

输出 q 个数字，每个数字占一行：其中第 i 个数字应表示满足如下条件的子区间 [x; y]（即 l__i ≤ x ≤ y ≤ r__i）的个数——仅包含区间 [x; y] 内顶点及其之间边所构成的子图是二分图。

The first example is shown on the picture below:

For the first query, all subsegments of [1; 3], except this segment itself, are suitable.

For the first query, all subsegments of [4; 6], except this segment itself, are suitable.

For the third query, all subsegments of [1; 6] are suitable, except [1; 3], [1; 4], [1; 5], [1; 6], [2; 6], [3; 6], [4; 6].

The second example is shown on the picture below:

第一个示例如下图所示：

对于第一个查询，区间 $[1; 3]$ 的所有子区间（除该区间本身外）均满足条件。

对于第二个查询，区间 $[4; 6]$ 的所有子区间（除该区间本身外）均满足条件。

对于第三个查询，区间 $[1; 6]$ 的所有子区间均满足条件，但以下子区间除外：$[1; 3]$、$[1; 4]$、$[1; 5]$、$[1; 6]$、$[2; 6]$、$[3; 6]$、$[4; 6]$。

第二个示例如下图所示：