Problem: There are N cells arranged in a row, numbered 1, 2, \ldots, N from left to right.

Tak lives in these cells and is currently on Cell 1. He is trying to reach Cell N by using the procedure described below.

You are given an integer K that is less than or equal to 10, and K non-intersecting segments [L_1, R_1], [L_2, R_2], \ldots, [L_K, R_K]. Let S be the union of these K segments. Here, the segment [l, r] denotes the set consisting of all integers i that satisfy l \leq i \leq r.

* When you are on Cell i, pick an integer d from S and move to Cell i + d. You cannot move out of the cells.



To help Tak, find the number of ways to go to Cell N, modulo 998244353.

Constraints

* 2 \leq N \leq 2 \times 10^5
* 1 \leq K \leq \min(N, 10)
* 1 \leq L_i \leq R_i \leq N
* [L_i, R_i] and [L_j, R_j] do not intersect (i \neq j)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
L_1 R_1
L_2 R_2
:
L_K R_K


Output

Print the number of ways for Tak to go from Cell 1 to Cell N, modulo 998244353.

Examples

Input

5 2
1 1
3 4


Output

4


Input

5 2
3 3
5 5


Output

0


Input

5 1
1 2


Output

5


Input

60 3
5 8
1 3
10 15


Output

221823067

Solution (in JAVA):

Solution:
import java.util.*;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int k = sc.nextInt();
		int mod = 998244353;
		
		int[] l = new int[k];
		int[] r = new int[k];
		long[] sum = new long[k];
		for(int i = 0; i < k; i++){
			l[i] = sc.nextInt();
			r[i] = sc.nextInt();
		}
		
		long[] dp = new long[n*2];
		dp[1] = 1;
		
		for(int i = 1; i <= n; i++){
			for(int j = 0; j < k; j++){
				int ra = Math.min(n, i - l[j]);
				ra = Math.max(0, ra);
				int la = Math.max(0, i - r[j]);
				la = Math.min(n, la);
				
				sum[j] += dp[ra];
				dp[i] += sum[j];
				sum[j] -= dp[la];
			}
			dp[i] %= mod;
		}
		System.out.println(dp[n]);
	}
}