Variable, or There and Back Again

Description:

Input:

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 10⁵) — the numbers of states and transitions, correspondingly.

The second line contains space-separated n integers f₁, f₂, ..., 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.

Output:

Print n integers r₁, r₂, ..., 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.

Sample Input:

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

Sample Output:

1
1
1
1

Sample Input:

3 1
1 0 2
1 3

Sample Output:

1
0
1

Sample Input:

3 1
2 0 1
1 3

Sample Output:

0
0
0

Note:

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.