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.Arrays;
import java.util.Scanner;

/**
 *
 * dp[i] 表示走到i点的方案数
 *
 * 因为只能在区间当中取数，同时对于每一个区间[a,b] , dp[b] = dp[i-b] + dp[i-b+1] + ...... + dp[i-a] （因为能取的数只有a~b）
 *
 * 因此转移方程为：
 *
 * i == 0 时 dp[i] = 1
 *
 * a[0] > i > 0
 *
 * dp[i] = 0;
 *
 * b[j] >= i >= a[j] 时：
 *
 * dp[i] = dp[i-a[j]] + ...... + dp[max(0,i-b[j])]
 *
 * 其他情况
 *
 * dp[i] = dp[i-1]
 *
 * Created by enpingkuang on 2020/9/19 7:53 下午
 */
public class Main {
    private static int MOD = 998244353;
    private static long[] dp = new long[200005];
    private static long[] sum = new long[200005];

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        int k = scanner.nextInt();
        int[] l = new int[200005];
        int[] r = new int[200005];
        for(int i = 0;i<k;i++){
             l[i] = scanner.nextInt();
             r[i] = scanner.nextInt();
        }
        dp[0] = 1;
        sum[0] = 1;
        for(int i=1;i<n;i++) {
            for(int j = 0;j<k;j++){
                if(i >= l[j]){
                    long flag = i-r[j]-1 < 0?0:sum[i-r[j]-1];
                    dp[i] = ((dp[i] + sum[i-l[j]] - flag)%MOD + MOD)%MOD;
                }
            }
            sum[i] = (sum[i-1] + dp[i])%MOD;
        }
        System.out.println(dp[n-1]);
    }
}