CF1276B.Two Fairs

There are $n$ cities in Berland and some pairs of them are connected by two-way roads. It is guaranteed that you can pass from any city to any other, moving along the roads. Cities are numerated from $1$ to $n$.

Two fairs are currently taking place in Berland — they are held in two different cities $a$ and $b$ ($1 \le a, b \le n$; $a \ne b$).

Find the number of pairs of cities $x$ and $y$ ($x \ne a, x \ne b, y \ne a, y \ne b$) such that if you go from $x$ to $y$ you will have to go through both fairs (the order of visits doesn't matter). Formally, you need to find the number of pairs of cities $x,y$ such that any path from $x$ to $y$ goes through $a$ and $b$ (in any order).

Print the required number of pairs. The order of two cities in a pair does not matter, that is, the pairs $(x,y)$ and $(y,x)$ must be taken into account only once.

伯兰有 $n$ 座城市，其中某些城市对之间由双向道路连接。保证任意两座城市之间均可通过道路相互到达。城市编号为 $1$ 到 $n$。

目前伯兰正在举办两场集市——分别位于两座不同的城市 $a$ 和 $b$（$1 \le a, b \le n$；$a \ne b$）。

请找出满足以下条件的城市对 $(x, y)$ 的数量：$x \ne a$，$x \ne b$，$y \ne a$，$y \ne b$，且从 $x$ 到 $y$ 的任意路径都必须经过这两座集市所在的城市 $a$ 和 $b$（访问顺序不限）。形式化地说，你需要找出满足如下条件的城市对 $(x, y)$ 的数量：任意一条从 $x$ 到 $y$ 的路径均同时经过 $a$ 和 $b$（顺序不限）。

请输出满足条件的城市对的数量。注意：城市对中两个城市的顺序无关紧要，即 $(x,y)$ 与 $(y,x)$ 视为同一对，仅计一次。

The first line of the input contains an integer $t$ ($1 \le t \le 4\cdot10^4$) — the number of test cases in the input. Next, $t$ test cases are specified.

The first line of each test case contains four integers $n$, $m$, $a$ and $b$ ($4 \le n \le 2\cdot10^5$, $n - 1 \le m \le 5\cdot10^5$, $1 \le a,b \le n$, $a \ne b$) — numbers of cities and roads in Berland and numbers of two cities where fairs are held, respectively.

The following $m$ lines contain descriptions of roads between cities. Each of road description contains a pair of integers $u_i, v_i$ ($1 \le u_i, v_i \le n$, $u_i \ne v_i$) — numbers of cities connected by the road.

Each road is bi-directional and connects two different cities. It is guaranteed that from any city you can pass to any other by roads. There can be more than one road between a pair of cities.

The sum of the values of $n$ for all sets of input data in the test does not exceed $2\cdot10^5$. The sum of the values of $m$ for all sets of input data in the test does not exceed $5\cdot10^5$.

输入的第一行包含一个整数 $t$（$1 \le t \le 4\cdot10^4$），表示输入中测试用例的数量。接下来给出 $t$ 个测试用例。

每个测试用例的第一行包含四个整数 $n$、$m$、$a$ 和 $b$（$4 \le n \le 2\cdot10^5$，$n - 1 \le m \le 5\cdot10^5$，$1 \le a,b \le n$，且 $a \ne b$），分别表示 Berland 国家的城市数量、道路数量，以及举办集市的两个城市的编号。

接下来的 $m$ 行描述城市之间的道路。每行包含一对整数 $u_i, v_i$（$1 \le u_i, v_i \le n$，$u_i \ne v_i$），表示由该道路连接的两座城市的编号。

每条道路均为双向道路，且连接两个不同的城市。保证任意两座城市之间均可通过道路相互到达。两座城市之间可能存在多条道路。

所有测试用例中 $n$ 的总和不超过 $2\cdot10^5$；所有测试用例中 $m$ 的总和不超过 $5\cdot10^5$。

Print $t$ integers — the answers to the given test cases in the order they are written in the input.

输出 $t$ 个整数——即按输入中给出的顺序，对应各测试用例的答案。