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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve();
    }
    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int K = scan.nextInt();
        int[] L = new int[K];
        int[] R = new int[K];
        for (int i = 0; i < K; i++) {
            L[i] = scan.nextInt();
            R[i] = scan.nextInt();
        }
        long mod = 998244353;
        long[] dp = new long[N+1];
        dp[1] = 1;
        dp[2] = -1;
        for (int i = 1; i <= N; i++) {
            if (1 < i) {
                dp[i] += dp[i - 1];
                dp[i] %= mod;
            }
            for (int j = 0; j < K; j++) {
                if (N < i + L[j]) {
                    continue;
                }
                dp[i + L[j]] += dp[i];
                dp[i + L[j]] %= mod;
                if (i + R[j] + 1 <= N) {
                    dp[i + R[j] + 1] -= dp[i];
                    dp[i + R[j] + 1] %= mod;
                    if (dp[i + R[j] + 1] < 0) {
                        dp[i + R[j] + 1] += mod;
                    }
                }
            }
        }
        System.out.println(dp[N]);
    }
}