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.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		long m=998244353;
		
		int n=s.nextInt();
		int k=s.nextInt();
		
		pair[] arr=new pair[n];
		
		for(int i=0;i<k;i++)
		{
			int l=s.nextInt();
			int r=s.nextInt();
			
			pair p=new pair(l,r);
			arr[i]=p;	
		}
		
		long[] dp=new long[n];
		
		for(int i=n-2;i>=0;i--)
		{
			for(int j=0;j<k;j++)
			{
				int min=i+arr[j].l;
				int max=i+arr[j].r;
				
				if(min>n-1)
				{
					
				}
				else if(max>=n-1)
				{
					dp[i]=(dp[i]%m+1%m)%m;
					
					max=n-2;
					
					if(max>=min)
					{
						dp[i]=(dp[i]%m+(dp[min]%m-dp[max+1]%m+m)%m)%m;
					}
					
				}
				else
				{
					dp[i]=(dp[i]%m+(dp[min]%m-dp[max+1]%m+m)%m)%m;
				}
				
			}
			
			dp[i]=(dp[i]%m+dp[i+1]%m)%m;
			
		}
		
		System.out.println((dp[0]%m-dp[1]%m+m)%m);
		
	}
	
}

class pair
{
	int l;
	int r;
	
	public pair(int l,int r)
	{
		this.l=l;
		this.r=r;
	}
}