Problem Description

This is a template problem.

There are $n$ nodes and $m$ edges. Each edge $e$ has a lower bound $\text{lower}(e)$ and an upper bound $\text{upper}(e)$. The task is to find a feasible solution such that all nodes satisfy flow balance conditions, and all edges satisfy flow restrictions.

Input Format

The first line contains two positive integers, $n$ and $m$.

The next $m$ lines each contain four integers: $s$, $t$, $\text{lower}$, and $\text{upper}$.

Output Format

If there is no solution, print a single line with NO.

Otherwise, print YES on the first line, followed by $m$ lines, each containing one integer representing the flow on each edge.

4 6
1 2 1 2
2 3 1 2
3 4 1 2
4 1 1 2
1 3 1 2
4 2 1 2

NO

4 6
1 2 1 3
2 3 1 3
3 4 1 3
4 1 1 3
1 3 1 3
4 2 1 3

YES
1
2
3
2
1
1

Constraints and Hints

$1 \leq n \leq 200, 1 \leq m \leq 10200, 1 \le s,t \le n, 0 \le \text{lower} \le \text{upper} < 3000$