Range Sum

Problem Description

Xiaohong has a secret array $A$ of length $N$. She will give you $Q$ hints; the $i$-th hint tells you the sum of the consecutive elements from $L_i$ to $R_i$ of array $A$. Can you determine, from these $Q$ hints, the sum of all elements of array $A$? If yes, output Yes; otherwise output No.

Input Format

The first line contains two integers $N$ and $q$; then there are $Q$ lines, each containing two integers $L_i$ and $R_i$.

Output Format

Output Yes or No, indicating whether the total sum can be determined.

Sample Input

4 3
1 3
1 2
2 3

Sample Output

No

Constraints

$1 \le N \le 2 \times 10^5$

$1 \le Q \le \min(2 \times 10^5, \frac{N(N+1)}{2})$

$1 \le L_i \le R_i \le N$

$(L_i, R_i) \neq (L_j, R_j)$ for $i \neq j$