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.IOException;
import java.io.InputStream;
import java.util.*;
import java.util.stream.IntStream;

public class Main {
	final static long MOD = 998244353L;
	
	class Node {
		HashMap<Integer, Long> V = new HashMap<>();
		
		void addP(int n){
			V.put(n, V.getOrDefault(n,0L)+1);
			if (V.get(n) == 0L) V.remove(n);
		}
		
		void addM(int n){
			V.put(n, V.getOrDefault(n,0L)-1);
			if (V.get(n) == 0L) V.remove(n);
		}
	}
	
	public Main() {
		FastScanner scanner = new FastScanner();
		int N = scanner.nextInt();
		int K = scanner.nextInt();
		
		int[][] S = new int[K][2];
		IntStream.range(0, K).forEach( i -> {
			S[i][0] = scanner.nextInt();
			S[i][1] = scanner.nextInt();
		});
		
		Node[] DP = new Node[N+1];
		IntStream.rangeClosed(1, N).forEach( i -> DP[i] = new Node());
		
		IntStream.range(1, N).forEach( i -> {
			IntStream.range(0, K).forEach(k -> {
				if (i+S[k][0]   <= N) DP[i+S[k][0]  ].addP(i);
				if (i+S[k][1]+1 <= N) DP[i+S[k][1]+1].addM(i);
			});
		});
		
		long NUM[] = new long[N+1];
		NUM[1] = 1L;
		long SUM = 0L;
		for (int n = 2; n <= N; n++) {
			for (int i : DP[n].V.keySet() ) {
				SUM = (SUM + NUM[i]*DP[n].V.get(i)%MOD) % MOD;
				if (SUM < 0) SUM += MOD;
			}
			NUM[n] = SUM;
		}
		
		System.out.println(NUM[N]);
	}
	
	public static void main(String[] args) {
		new Main();
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;
	
	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}
	
	private int readByte() {
		if (hasNextByte()) return buffer[ptr++];
		else return -1;
	}
	
	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}
	
	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		return hasNextByte();
	}
	
	public String next() {
		if (!hasNext()) throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	public long nextLong() {
		if (!hasNext()) throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}
	
	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
		return (int) nl;
	}
	
	public double nextDouble() {
		return Double.parseDouble(next());
	}
}