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.*;

public class Main {

    private static long getSum(int l, int r, long[] sum) {
        long ans = r >= 0 ? sum[r] : 0;
        ans -= l >= 0 ? sum[l] : 0;
        return ans;
    }

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        long mod = 998244353L;
        int n = scan.nextInt();
        int k = scan.nextInt();
        int[] l = new int[n];
        int[] r = new int[n];
        for (int i = 0; i < k; i++) {
            l[i] = scan.nextInt();
            r[i] = scan.nextInt();
        }
        long[] sum = new long[n];
        long[] dp = new long[n];
        sum[0] = dp[0] = 1;
        for (int i = 1; i < n; i++) {
            for (int j = 0; j < k; j++) {
                dp[i] = (dp[i] + getSum(i - r[j] - 1, i - l[j], sum)) % mod;
            }
            sum[i] = sum[i - 1] + dp[i];
        }
        System.out.println(dp[n - 1]);
    }
}