Build a Tree and That Is It

Description:

Input:

The first line of the input contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) —the number of test cases in the test.

This is followed by $$$t$$$ test cases, each written on a separate line.

Each test case consists of four positive integers $$$n, d_{12}, d_{23}$$$ and $$$d_{31}$$$ ($$$3 \le n \le 2\cdot10^5; 1 \le d_{12}, d_{23}, d_{31} \le n-1$$$).

It is guaranteed that the sum of $$$n$$$ values for all test cases does not exceed $$$2\cdot10^5$$$.

Output:

For each test case, print YES if the suitable tree exists, and NO otherwise.

If the answer is positive, print another $$$n-1$$$ line each containing a description of an edge of the tree — a pair of positive integers $$$x_i, y_i$$$, which means that the $$$i$$$th edge connects vertices $$$x_i$$$ and $$$y_i$$$.

The edges and vertices of the edges can be printed in any order. If there are several suitable trees, output any of them.

Sample Input:

9
5 1 2 1
5 2 2 2
5 2 2 3
5 2 2 4
5 3 2 3
4 2 1 1
4 3 1 1
4 1 2 3
7 1 4 1

Sample Output:

YES
1 2
4 1
3 1
2 5
YES
4 3
2 5
1 5
5 3
NO
YES
2 4
4 1
2 5
5 3
YES
5 4
4 1
2 5
3 5
YES
2 3
3 4
1 3
NO
YES
4 3
1 2
2 4
NO