Problem Statement

You are given integers $N$ and $K$.

The cumulative sums of an integer sequence $X=(X_1,X_2,\dots ,X_N)$ of length $N$ is defined as a sequence $Y=(Y_0,Y_1,\dots ,Y_N)$ of length $N+1$ as follows:

• $Y_0=0$
• $Y_i=\displaystyle\sum_{j=1}^{i}X_j\ (i=1,2,\dots ,N)$

An integer sequence $X=(X_1,X_2,\dots ,X_N)$ of length $N$ is called a good sequence if and only if it satisfies the following condition:

• Any value in the cumulative sums of $X$ that is less than $K$ appears before any value that is not less than $K$.
• Formally, for the cumulative sums $Y$ of $X$, for any pair of integers $(i,j)$ such that $0 \le i,j \le N$, if $(Y_i < K$ and $Y_j \ge K)$, then $i < j$.

You are given an integer sequence $A=(A_1,A_2,\dots ,A_N)$ of length $N$. Determine whether the elements of $A$ can be rearranged to a good sequence. If so, print one such rearrangement.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $-10^9 \leq K \leq 10^9$
• $-10^9 \leq A_i \leq 10^9$
• All input values are integers.

Input

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

N K
A_1 A_2 \cdots A_N

Output

If the elements of $A$ can be rearranged to a good sequence, print the rearranged sequence $(A^{\prime}_1,A^{\prime}_2,\dots ,A^{\prime}_N)$ in the following format:

Yes
A^{\prime}_1 A^{\prime}_2 \cdots A^{\prime}_N

If there are multiple valid rearrangements, any of them is considered correct.

If a good sequence cannot be obtained, print No.