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).
First line contains two integers $n$ and $m$ ($ 1 \leq n \times m \leq 10^5 $).
For each question, print "YES" if the solution exists, or "NO" otherwise.