Problem Statement

Giving photos to Friends makes the Friends stronger. How this works is a mystery.

Photos have special effects and are divided into $2$ types according to their activation conditions. Here, we simply call them type $1$ and type $2$.

There are $N$ Friends, numbered $1,2,\dots,N$.

The Captain has $P$ photos of type $1$ and $Q$ photos of type $2$. Friend $i$ wants to hold $X_i$ photos, but can hold at most $A_i$ photos of type $1$ and at most $B_i$ photos of type $2$.

The Captain wonders whether it is possible to give photos to the Friends so as to meet all of their wishes. Determine whether it is possible to give each Friend exactly $X_i$ photos, and if it is possible, output one such way.

Constraints

• $1\leq N\leq 2\times 10^5$
• $0\leq P,Q\leq 10^{18}$
• $1\leq X_i\leq 10^9$
• $0\leq A_i,B_i\leq 10^9$
• All input values are integers.

Input

$N$ $P$ $Q$
$X_1$ $A_1$ $B_1$
$X_2$ $A_2$ $B_2$
$\vdots$
$X_N$ $A_N$ $B_N$

Output

If there is no way of giving photos that satisfies the conditions, output No.

If there is one, output $N+1$ lines.

On line $1$, output Yes. On line $i+1$, output the number of type $1$ photos and the number of type $2$ photos given to Friend $i$, in this order, separated by a space.

If there are multiple ways of giving photos, any of them will be accepted.

Sample

3 3 4
2 2 1
3 3 2
2 0 2

Yes
1 1
2 1
0 2

3 3 4
2 1 2 
3 1 3
2 0 2

No