Problem Statement

For two $N \times N$ matrices $A$ and $B$ whose elements are $0$ or $1$, we say that $A$ and $B$ are similar if they satisfy the following conditions:

• The sums of corresponding rows are equal. That is, $A_{i,1} + \dots + A_{i,N} = B_{i,1} + \dots + B_{i,N}$ for any $i=1,\dots,N$.
• The sums of corresponding columns are equal. That is, $A_{1,j} + \dots + A_{N,j} = B_{1,j} + \dots + B_{N,j}$ for any $j=1,\dots,N$.

Furthermore, for an $N \times N$ matrix $A$ whose elements are $0$ or $1$, and integers $i,j$ ($1 \leq i,j \leq N$), we say that the element at row $i$ column $j$ is fixed if $A_{i,j} = B_{i,j}$ holds for any matrix $B$ that is similar to $A$.

Answer the following $Q$ queries:

• The $i$-th query: If there exists an $N \times N$ matrix whose elements are $0$ or $1$ such that exactly $K_i$ elements are fixed, output Yes; otherwise, output No.

Constraints

• $2 \le N \le 30$
• $1 \le Q \le N^2+1$
• $0 \le K_i \le N^2$
• $K_i \ne K_j (1 \le i < j \le Q)$
• All inputs are integers

Input

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

N Q
K_1
K_2
\vdots
K_Q

Output

Output $Q$ lines. For the $i$-th line $(1 \le i \le Q)$, output the answer for the $i$-th query.