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There is a matrix $X$ with $ n \times m $ cells where each cell has an associated weight. A subset $S$ of cells is considered connected if, between every pair of cells in $S$, there is a path of neighboring cells, also in $S$, that joins them. Two cells are considered neighboring if they share a side. The weight of a subset $S$ is the sum of the weights of the cells that are in $S$.
You are asked to answer several queries, where each query has a weight of $k$. For each query, determine whether there is a connected subset whose weight is between $k$ and $ 2 \cdot k$ (inclusive).
Input
First line contains two integers $n$ and $m$ ($ 1 \leq n \times m \leq 10^5 $).
Then $n$ lines each with $m$ integers. The $j$-th number in the $i$-th line represents the weight of the cell $ X[i, j]$ ($ 1 \leq X [i, j] \leq 10^9 $).
Output
For each question, print "YES" if the solution exists, or "NO" otherwise.
Sample test(s)
Input
3 4
1 1 9 2
9 9 9 9
1 1 9 1
10
1
2
3
4
5
6
7
8
9
10
Output
YES
YES
NO
NO
YES
YES
YES
YES
YES
YES
Input
5 5
8 9 1 9 4
941 942 8 4 2
5 939 921 978 914
932 1 8 9 4
7 3 6 5 10
4
450
58
20
10
Output
NO
NO
YES
YES