Takahashi has a secret integer sequence $a$. You know that the length of $a$ is $N$. You want to guess the contents of $a$. He has promised to give you the following $Q$ additional pieces of information. - The $i$-th information: the value $a_{l_i} + a_{l_i+1} + \dots + a_{r_i}$. Is it possible to determine the sum of all elements in $a$, $a_1 + a_2 + \dots + a_N$, if the $Q$ pieces of promised information are given?

Input is given from Standard Input in the following format: > $N \quad Q$\ > $l_1 \quad r_1$\ > $l_2 \quad r_2$\ > $\vdots$\ > $l_Q \quad r_Q$ #### Constraints - $1 \leq N \leq 2 \times 10^5$ - $1 \leq Q \leq \min(2 \times 10^5, \frac{N(N+1)}{2})$ - $1 \leq l_i \leq r_i \leq N$ - $(l_i, r_i)\neq(l_j, r_j)$ $(i \neq j)$ - All values in input are integers.

If it is possible to determine the sum of all elements in $a$, print `Yes`; otherwise, print `No`.

***For Sample #1:*** From the first and second information, we can find the value $a_1 + a_2 + a_2 + a_3$. By subtracting the value of $a_2$ from it, we can determine the value $a_1 + a_2 + a_3$. ***For Sample #2:*** We can determine the sum of the first $3$ elements of $a$, but not the sum of all elements. ***For Sample #3:*** The fourth information directly gives us the sum of all elements.

AtCoder [ABC238E]