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.ArrayList;
import java.util.Collections;
import java.util.Scanner;

public class Main {
	public static void main(String args[]) {
		Scanner stdIn = new Scanner(System.in);
		int mod = 998244353;
		int N = stdIn.nextInt();
		int K = stdIn.nextInt();
		ArrayList<Integer> L = new ArrayList<Integer>();
		ArrayList<Integer> R = new ArrayList<Integer>();
		for(int i = 0; i < K; i ++) {
			L.add(stdIn.nextInt());
			R.add(stdIn.nextInt());
		}
		
		ArrayList<Long> A = new ArrayList<Long>();
		A.add((long) 0);
		A.add((long) 1);
		ArrayList<Long> Sum = new ArrayList<Long>();
		Sum.add((long) 0);
		Sum.add((long) 1);
		
		for(int i = 2; i <= N; i ++) {
			long addNum = 0;
			for(int j = 0; j < K; j ++) {
				int idxL = i - R.get(j) - 1;
				int idxR = i - L.get(j);
				if(idxR <= 0) {
					continue;
				}else if(idxL < 0 && 0 <idxR) {
					addNum += (Sum.get(idxR) - Sum.get(0)) % mod;
				}else {
					addNum += (Sum.get(idxR) - Sum.get(idxL)) % mod;
				}
			}
			A.add(addNum);
			Sum.add(Sum.get(Sum.size() - 1) + addNum);
		}
      
		System.out.println(A.get(A.size() - 1) % mod);
	}
}