You are given two integers $b$ and $w$. You have a chessboard of size $10^9 \times 10^9$ with the top left cell at $(1; 1)$, the cell $(1; 1)$ is painted white.

Your task is to find a connected component on this chessboard that contains exactly $b$ black cells and exactly $w$ white cells. Two cells are called connected if they share a side (i.e. for the cell $(x, y)$ there are at most four connected cells: $(x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1)$). A set of cells is called a connected component if for every pair of cells $C_1$ and $C_2$ from this set, there exists a sequence of cells $c_1$, $c_2$, ..., $c_k$ such that $c_1 = C_1$, $c_k = C_2$, all $c_i$ from $1$ to $k$ are belong to this set of cells and for every $i \in [1, k - 1]$, cells $c_i$ and $c_{i + 1}$ are connected.

Obviously, it can be impossible to find such component. In this case print "NO". Otherwise, print "YES" and any suitable connected component.

You have to answer $q$ independent queries.