Brick Tower

There are $N$ children in Luca’s kindergarten, numbered from $0$ to $N −1$. Child $i$ (for each $i = 0, 1, \dots , N −1$) has a toy brick with height $H_i$.

Today, Luca asked the children to build a tower of height $S$. To do so, some of the children may stack their bricks on top of one another so that the total height of the selected bricks is exactly $S$.

However, the children prefer to keep their bricks for themselves. For each child, determine whether their brick is indispensable. That is, whether it is impossible to build a tower of height S without using that child’s brick.

Input data

The first line of the input file contains two integers: $N$ and $S$, respectively the number of children and the height of the tower to build.

The second line of the input file contains $N$ integers: $H_0, H_1, \dots , H_{N−1}$, the heights of the bricks.

Output data

The output file must contain $N$ lines, each consisting of a single string: the $i$-th line must be YES if the brick of child $i$ is indispensable, and NO otherwise.

Constraints and clarifications

• $1 \leq N \leq 3000$.
• $1 \leq S \leq 3000$.
• $1 \leq H_i \leq S$ for each $i = 0, 1, \dots , N − 1$.
• There is at least one way to build a tower of height $S$ using some of the bricks.

Example 1

stdin

3 7
3 4 4

stdout

YES
NO
NO

Explanation

In the first sample case, the only ways to build a tower of height $7$ is to use the brick of child $0$ combined with one of the other children’s bricks. Therefore, only the brick of child $0$ is indispensable.

Example 2

stdin

5 10
5 1 4 2 2

stdout

YES
YES
NO
NO
NO

Explanation

In the second sample case, it can be proven that only the brick of child $0$ and child $1$ is indispensable.