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:
//package src.com.jetman.atcoder;

import java.util.*;

/**
 * @description:
 * @author: Jetman
 * @create: 2020-08-29 14:39
 **/
public class Main {

    Scanner sc = new Scanner(System.in);

    long MOD = 998244353L;

    long dp[];

    private void slove() {

        int n = sc.nextInt();
        int k = sc.nextInt();

        int[][] a = new int[k][2];
        for (int i = 0; i < k; i++) {
            a[i][0] = sc.nextInt();
            a[i][1] = sc.nextInt();
        }

        dp = new long[n+1];
        dp[1] = 1;
        long[] sum = new long[n+1];
        sum[1] = 1;
        for (int i = 2; i <= n ; i++) {
            long tmp = 0;
            for (int j = 0; j < k; j++) {
                int l = i - a[j][1] > 0 ? i - a[j][1]-1 : 0;
                int r = i - a[j][0] > 0 ? i - a[j][0] : 0;
                dp[i] = (dp[i] + sum[r] - sum[l] + MOD)%MOD;
            }
            sum[i] = (sum[i-1] + dp[i])%MOD;
        }


        System.out.println(dp[n]);



    }

    private void build(Map<Integer, List<Integer>> edge, int l, int r) {
        List<Integer> list = edge.getOrDefault(l, new ArrayList<>());
        list.add(r);
        edge.put(l,list);
    }


    public static void main(String[] args) {
        new Main().slove();
    }
}