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.*;
import java.io.*;
import java.nio.charset.StandardCharsets;

public class Main {

	public static void main(String[] args) throws IOException {
		InputStreamReader reader = new InputStreamReader(System.in, StandardCharsets.UTF_8);
		BufferedReader in = new BufferedReader(reader);
		Main ins = new Main(in);
		ins.calc();
		ins.showResult();
	}

	int N, K;
	int[] L, R;
	long MOD = 998244353L;
	long[] memo;

	Main(BufferedReader in) throws IOException {
		String[] tokens = in.readLine().split(" ");
		N = Integer.parseInt(tokens[0]);
		K = Integer.parseInt(tokens[1]);
		L = new int[K];
		R = new int[K];
		for (int i = 0; i < K; ++i) {
			tokens = in.readLine().split(" ");
			L[i] = Integer.parseInt(tokens[0]);
			R[i] = Integer.parseInt(tokens[1]);
		}
		memo = new long[N];
		Arrays.fill(memo, 0L);
		memo[0] = 1L;
	}

	void calc() {
		long[] diffs = new long[N];
		Arrays.fill(diffs, 0L);
		diffs[1] = -1L;
		for (int i = 0; i + 1 < N; ++i) {
			for (int k = 0; k < K; ++k) {
				int l = i + L[k];
				int r = i + R[k] + 1;
				if (l < N) {
					diffs[l] += memo[i] + MOD;
					diffs[l] %= MOD;
				}
				if (r < N) {
					diffs[r] -= memo[i] + MOD;
					diffs[r] %= MOD;
				}
			}
			memo[i + 1] = memo[i] + diffs[i + 1];
			memo[i + 1] += MOD;
			memo[i + 1] %= MOD;
		}
	}

	void showResult() {
		System.out.println(memo[N - 1]);
	}
}