Problem Statement

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 $a_{l_i}+a_{l_i+1}+\\cdots+a_{r_i}$.

Is it possible to determine the sum of all elements in $a$, $a_1+a_2+\\cdots+a_N$, if the $Q$ pieces of promised information are given?

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.

Input

Input is given from Standard Input in the following format:

$N$ $Q$ $l_1$ $r_1$ $l_2$ $r_2$ $\\hspace{0.4cm}\\vdots$ $l_Q$ $r_Q$

Output

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

Sample Input 1

3 3
1 2
2 3
2 2

Sample Output 1

Yes

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 $a_1+a_2+a_3$.

Sample Input 2

4 3
1 3
1 2
2 3

Sample Output 2

No

We can determine the sum of the first $3$ elements of $a$, but not the sum of all elements.

Sample Input 3

4 4
1 1
2 2
3 3
1 4

Sample Output 3

Yes

The fourth information directly gives us the sum of all elements.