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?

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.

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.

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.

见题面 Input 部分

见题面 Output 部分