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) {
        final int mod = 998244353;
        final Scanner sc = new Scanner(System.in);
        final int n = sc.nextInt();
        final int k = sc.nextInt();
        final int[][] data = new int[k][2];
        for (int i = 0; i < k; i++) {
            data[i][0] = sc.nextInt();
            data[i][1] = sc.nextInt() + 1;
        }
        final long[] dp = new long[n];
        dp[0] = 1;
        dp[1] = -1;
        for (int i = 0; i < n; i++) {
            if (i != 0) { 
                dp[i] = (dp[i] + dp[i - 1]) % mod;
            }
            for (int j = 0; j < k; j++) {
                final int l = data[j][0] + i;
                final int r = data[j][1] + i;
                if (l < n) { 
                    dp[l] = (dp[l] + dp[i]) % mod;
                }
                if (r < n) { 
                    dp[r] = (dp[r] - dp[i] + mod) % mod;
                }
            }
        }
        System.out.println(dp[n - 1]);
    }
}