Variable, or There and Back Again

题意翻译

## 题目描述 给你一个n个点，m条边的有向图（不一定连通），每个点都被标上了0、1或2。如果有一条路径是从一个标为1的点开始，途径若干个标为0或2的点，最后到达一个标为2的点，那么这条路径上的所有点都算作被访问过。请问最后有多少点被访问过？ ## 输入格式 共m+2行。 第一行，2个整数n和m(1<=n,m<=100000),表示有向图的点数和边数。 第二行，n个整数f1，f2……fn(0<=fi<=2),表示第i个点标记的数——0、1或2。 接下来m行，每行2个整数ai，bi (1<=ai,bi<=n，ai不等于bi),表示从第ai个点到第bi个点有一条边。 ## 输出格式 共n行，每行一个整数ri，若ri=1表示第i个点被访问过，否则ri=0。 ## 说明/提示 对于样例1，唯一的合法路径1->2->3->4包含了全部的点。 对于样例2，唯一的一条合法路径3->1包含了1和3两个点，点2没有在路径中。 对于样例3，没有一条路径是合法的。

题目描述

Life is not easy for the perfectly common variable named Vasya. Wherever it goes, it is either assigned a value, or simply ignored, or is being used! Vasya's life goes in states of a program. In each state, Vasya can either be used (for example, to calculate the value of another variable), or be assigned a value, or ignored. Between some states are directed (oriented) transitions. A path is a sequence of states $ v_{1},v_{2},...,v_{x} $ , where for any $ 1<=i&lt;x $ exists a transition from $ v_{i} $ to $ v_{i+1} $ . Vasya's value in state $ v $ is interesting to the world, if exists path $ p_{1},p_{2},...,p_{k} $ such, that $ p_{i}=v $ for some $ i $ $ (1<=i<=k) $ , in state $ p_{1} $ Vasya gets assigned a value, in state $ p_{k} $ Vasya is used and there is no state $ p_{i} $ (except for $ p_{1} $ ) where Vasya gets assigned a value. Help Vasya, find the states in which Vasya's value is interesting to the world.

输入输出格式

输入格式

The first line contains two space-separated integers $ n $ and $ m $ ( $ 1<=n,m<=10^{5} $ ) — the numbers of states and transitions, correspondingly. The second line contains space-separated $ n $ integers $ f_{1},f_{2},...,f_{n} $ ( $ 0<=f_{i}<=2 $ ), $ f_{i} $ described actions performed upon Vasya in state $ i $ : $ 0 $ represents ignoring, $ 1 $ — assigning a value, $ 2 $ — using. Next $ m $ lines contain space-separated pairs of integers $ a_{i},b_{i} $ ( $ 1<=a_{i},b_{i}<=n $ , $ a_{i}≠b_{i} $ ), each pair represents the transition from the state number $ a_{i} $ to the state number $ b_{i} $ . Between two states can be any number of transitions.

输出格式

Print $ n $ integers $ r_{1},r_{2},...,r_{n} $ , separated by spaces or new lines. Number $ r_{i} $ should equal $ 1 $ , if Vasya's value in state $ i $ is interesting to the world and otherwise, it should equal $ 0 $ . The states are numbered from $ 1 $ to $ n $ in the order, in which they are described in the input.

输入输出样例

输入样例 #1

4 3
1 0 0 2
1 2
2 3
3 4

输出样例 #1

1
1
1
1

输入样例 #2

3 1
1 0 2
1 3

输出样例 #2

1
0
1

输入样例 #3

3 1
2 0 1
1 3

输出样例 #3

0
0
0

说明

In the first sample the program states can be used to make the only path in which the value of Vasya interests the world, 1  2  3  4; it includes all the states, so in all of them Vasya's value is interesting to the world. The second sample the only path in which Vasya's value is interesting to the world is , — 1  3; state 2 is not included there. In the third sample we cannot make from the states any path in which the value of Vasya would be interesting to the world, so the value of Vasya is never interesting to the world.