In the first line, output "No" (without quotes) if Sasha cannot achieve that all sheep move uniformly. Otherwise, output "Yes" (without quotes).

If $T = 2$ or $T = 3$, then in the second line output the maximum number of columns that Sasha can leave on the field so that all sheep move uniformly. If $T=1$, then \textbf{this should not be output}.

If $T = 3$, in the third line output the number $q$ ($0 \leq q \leq 10^6$) --- how many times Sasha will need to trim the field. In the next $q$ lines, output the description of the trimmings.

For the description of each trimming of the field, output in one line two integers $t$ and $x$ ($0 \leq t \leq 10^{18}$, $1 \leq x < m$), where $t$ is the time at which Sasha needs to trim the field (from the very beginning of the sheep's movement), and $x$ is the number of columns that will remain on the field after this operation.

The operations must be output in non-decreasing order of $t$. In each subsequent trimming, $x$ must be less than in the previous one.

If there are multiple suitable sequences of trimmings, any of them can be output.

It can be shown that under the given constraints, if a solution exists, then there exists a solution that fits within the given limits.

In case $T = 1$ or $T = 2$, do not output the description of the trimmings.