Problem Statement

Construct an undirected simple graph with $N$ vertices and $\displaystyle \frac{N(N-1)}{2}$ edges, that is, a complete graph on $N$ vertices, satisfying the following conditions.

• The cost of each edge is an integer between $0$ and $100$, inclusive.
• When starting from vertex $1$, passing through every vertex exactly $1$ time, and returning to vertex $1$, the sum of the costs of all edges traversed is always $T$.

You are given $Q$ test cases. Find the answer for each of them.

Input

$Q$
$N_1 \quad T_1$
$N_2 \quad T_2$
$\vdots$
$N_Q \quad T_Q$

• The input consists of integers.
• $1 \le Q \le 200$
• $2 \le N \le 8$
• $0 \le T \le 100$

Output

Let $S_i$ be the $i$-th answer. Output the results of the test cases separated by newlines, as follows.

$S_1$
$S_2$
$\vdots$
$S_Q$

For each test case, output as follows.

• If a graph satisfying the conditions exists, output Yes. On the $i$-th of the following $\displaystyle \frac{N(N-1)}{2}$ lines, output $a_i \ b_i \ c_i$. This means that the $i$-th edge of the graph connects $a_i$ and $b_i$ and has cost $c_i$. The following conditions must be satisfied.
  • $1 \le a_i < b_i \le N$
  • If $i \neq j$, then $(a_i,b_i) \neq (a_j,b_j)$
  • $0 \le c_i \le 100$
  • When starting from vertex $1$, passing through every vertex exactly $1$ time, and returning to vertex $1$, the sum of the costs of all edges traversed is always $T$.


• If no graph satisfying the conditions exists, output only No.

Sample

1
4 4

Yes
1 2 1
1 3 1
1 4 1
2 3 1
2 4 1
3 4 1