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;

public class Main {

	static final long mod = 998244353;

	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			int N = sc.nextInt();
			int K = sc.nextInt();
			Pair[] pairs = new Pair[K];
			for (int i = 0; i < K; i++) {
				int from = sc.nextInt();
				int to = sc.nextInt();
				pairs[i] = new Pair(from, to);
			}
			Arrays.sort(pairs);
			int idx = K;
			long[] arr = new long[N + 1];
			long[] sum = new long[N + 1];
			arr[1] = 1;
			sum[1] = 1;
			for (int i = 2; i <= N; i++) {
				for (int j = 0; j < idx; j++) {
					if (pairs[j].x >= i) {
						continue;
					}
					int from = Math.max(0, i - pairs[j].y - 1);
					arr[i] += (sum[i - pairs[j].x] - sum[from]);
					arr[i] %= mod;
				}
				sum[i] = (sum[i - 1] + arr[i]) % mod;
			}
			System.out.println((arr[N] + mod) % mod);
		}
	}

	static class Pair implements Comparable {
		int x;
		int y;

		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(Object x) {
			Pair other = (Pair) x;
			return this.x > other.x ? 1 : -1;
		}
	}
}