CF1472G.Moving to the Capital

There are $n$ cities in Berland. The city numbered $1$ is the capital. Some pairs of cities are connected by a one-way road of length 1.

Before the trip, Polycarp for each city found out the value of $d_i$ — the shortest distance from the capital (the $1$-st city) to the $i$-th city.

Polycarp begins his journey in the city with number $s$ and, being in the $i$-th city, chooses one of the following actions:

1. Travel from the $i$-th city to the $j$-th city if there is a road from the $i$-th city to the $j$-th and $d_i \lt d_j$;
2. Travel from the $i$-th city to the $j$-th city if there is a road from the $i$-th city to the $j$-th and $d_i \geq d_j$;
3. Stop traveling.

Since the government of Berland does not want all people to come to the capital, so Polycarp no more than once can take the second action from the list. in other words, he can perform the second action $0$ or $1$ time during his journey. Polycarp, on the other hand, wants to be as close to the capital as possible.

For example, if $n = 6$ and the cities are connected, as in the picture above, then Polycarp could have made the following travels (not all possible options):

• $2 \rightarrow 5 \rightarrow 1 \rightarrow 2 \rightarrow 5$;
• $3 \rightarrow 6 \rightarrow 2$;
• $1 \rightarrow 3 \rightarrow 6 \rightarrow 2 \rightarrow 5$.

Polycarp wants for each starting city $i$ to find out how close he can get to the capital. More formally: he wants to find the minimal value of $d_j$ that Polycarp can get from the city $i$ to the city $j$ according to the rules described above.

Berland 有 $n$ 座城市，编号为 $1$ 的城市是首都。某些城市对之间由一条长度为 $1$ 的单向道路连接。

旅行前，Polycarp 对每座城市 $i$ 计算出了 $d_i$ —— 从首都（即第 $1$ 号城市）到第 $i$ 号城市的最短距离。

Polycarp 从编号为 $s$ 的城市出发，在位于第 $i$ 号城市时，他可选择以下动作之一：

1. 若存在一条从第 $i$ 号城市指向第 $j$ 号城市的道路，且满足 $d_i \lt d_j$，则从第 $i$ 号城市前往第 $j$ 号城市；
2. 若存在一条从第 $i$ 号城市指向第 $j$ 号城市的道路，且满足 $d_i \geq d_j$，则从第 $i$ 号城市前往第 $j$ 号城市；
3. 停止旅行。

由于 Berland 政府不希望所有人都涌向首都，因此 Polycarp 至多只能执行一次 上述第 2 类动作；换言之，他在整个旅途中执行第 2 类动作的次数为 $0$ 或 $1$ 次。而 Polycarp 自身则希望尽可能靠近首都。

例如，若 $n = 6$，且各城市之间的连接关系如上图所示，则 Polycarp 可能进行如下行程（并非全部可能方案）：

• $2 \rightarrow 5 \rightarrow 1 \rightarrow 2 \rightarrow 5$；
• $3 \rightarrow 6 \rightarrow 2$；
• $1 \rightarrow 3 \rightarrow 6 \rightarrow 2 \rightarrow 5$。

Polycarp 希望对每个起始城市 $i$，求出他所能达到的、离首都最近的距离。更准确地说：他希望对每个起始城市 $i$，找出在上述规则下，从城市 $i$ 出发所能到达的城市 $j$ 中，$d_j$ 的最小可能值。

The first line contains one integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases. Then $t$ test cases follow.

Each test case is preceded by an empty line.

The first line of each test case contains two integers $n$ ($2 \leq n \leq 2 \cdot 10^5$) and $m$ ($1 \leq m \leq 2 \cdot 10^5$) — number of cities and roads, respectively.

This is followed by $m$ lines describing the roads. Each road is characterized by two integers $u$ and $v$ ($1 \leq u, v \leq n, u \ne v$) — the numbers of cities connected by a one-way road.

It is guaranteed that the sums of $n$ and $m$ over all test cases do not exceed $2 \cdot 10^5$.

It is guaranteed that for each pair of different cities $(u, v)$ there is at most one road from $u$ to $v$ (but a pair of roads from $u$ to $v$ and from $v$ to $u$ — is valid).

It is guaranteed that there is a path from the capital to all cities.

第一行包含一个整数 $t$（$1 \leq t \leq 10^4$）—— 测试用例的数量。随后是 $t$ 个测试用例。

每个测试用例之前有一空行。

每个测试用例的第一行包含两个整数 $n$（$2 \leq n \leq 2 \cdot 10^5$）和 $m$（$1 \leq m \leq 2 \cdot 10^5$）—— 分别表示城市的数量和道路的数量。

接下来是 $m$ 行，每行描述一条道路。每条道路由两个整数 $u$ 和 $v$（$1 \leq u, v \leq n,\ u \ne v$）表征，表示存在一条从城市 $u$ 到城市 $v$ 的单向道路。

保证所有测试用例的 $n$ 之和与 $m$ 之和均不超过 $2 \cdot 10^5$。

保证对于任意两个不同的城市 $(u, v)$，至多存在一条从 $u$ 到 $v$ 的道路（但同时存在从 $u$ 到 $v$ 和从 $v$ 到 $u$ 的两条道路是允许的）。

保证从首都到所有城市均存在路径。

For each test case, on a separate line output $n$ numbers, the $i$-th of which is equal to the minimum possible distance from the capital to the city where Polycarp ended his journey.

对于每个测试用例，在单独一行中输出 $n$ 个数字，其中第 $i$ 个数字等于 Polycarp 旅程结束时所在城市到首都的最小可能距离。