President and Roads

Description:

Input:

The first lines contain four integers n, m, s and t (2 ≤ n ≤ 10⁵; 1 ≤ m ≤ 10⁵; 1 ≤ s, t ≤ n) — the number of cities and roads in Berland, the numbers of the capital and of the Presidents' home town (s ≠ t).

Next m lines contain the roads. Each road is given as a group of three integers a_i, b_i, l_i (1 ≤ a_i, b_i ≤ n; a_i ≠ b_i; 1 ≤ l_i ≤ 10⁶) — the cities that are connected by the i-th road and the time needed to ride along it. The road is directed from city a_i to city b_i.

The cities are numbered from 1 to n. Each pair of cities can have multiple roads between them. It is guaranteed that there is a path from s to t along the roads.

Output:

Print m lines. The i-th line should contain information about the i-th road (the roads are numbered in the order of appearance in the input).

If the president will definitely ride along it during his travels, the line must contain a single word "YES" (without the quotes).

Otherwise, if the i-th road can be repaired so that the travel time on it remains positive and then president will definitely ride along it, print space-separated word "CAN" (without the quotes), and the minimum cost of repairing.

If we can't make the road be such that president will definitely ride along it, print "NO" (without the quotes).

Sample Input:

6 7 1 6
1 2 2
1 3 10
2 3 7
2 4 8
3 5 3
4 5 2
5 6 1

Sample Output:

YES
CAN 2
CAN 1
CAN 1
CAN 1
CAN 1
YES

Sample Input:

3 3 1 3
1 2 10
2 3 10
1 3 100

Sample Output:

YES
YES
CAN 81

Sample Input:

2 2 1 2
1 2 1
1 2 2

Sample Output:

YES
NO

Note:

The cost of repairing the road is the difference between the time needed to ride along it before and after the repairing.

In the first sample president initially may choose one of the two following ways for a ride: 1 → 2 → 4 → 5 → 6 or 1 → 2 → 3 → 5 → 6.