Score : $400$ points

Problem Statement

There are $N$ cards with an integer written on each side. Card $i$ $(1 \leq i \leq N)$ has an integer $a_i$ written on the front and an integer $b_i$ written on the back.

You may choose whether to place each card with its front or back side visible.

Determine if you can place the cards so that the sum of the visible integers exactly equals $S$. If possible, find a placement of the cards to realize it.

Constraints

• $1 \leq N \leq 100$
• $1 \leq S \leq 10000$
• $1 \leq a_i, b_i \leq 100 \, (1 \leq i \leq N)$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $S$

$a_1$ $b_1$

$\vdots$

$a_N$ $b_N$

Output

First, print Yes if you can make the sum of the visible integers exactly equal $S$, and No otherwise, followed by a newline.

Additionally, if such a placement is possible, print a string of length $N$ consisting of H and T that represents the placement of the cards to realize it. The $i$-th $(1 \leq i \leq N)$ character should be H if the $i$-th card should be placed with its front side visible, and T with its back. If there are multiple possible placements to realize the sum, printing any of them is accepted.

3 11
1 4
2 3
5 7

Yes
THH

For example, the following placements make the sum of the visible integers exactly equal $S (= 11)$:

• Place the $1$-st card with its front side visible, $2$-nd with its back, and $3$-rd with its back.
• Place the $1$-st card with its back side visible, $2$-nd with its front, and $3$-rd with its front.

Therefore, outputs like HTT and THH are accepted.

5 25
2 8
9 3
4 11
5 1
12 6

No

You cannot place the cards so that the sum of the visible integers exactly equals $S (= 25)$.