Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 2
1 1
3 4

Sample Output 1

4

The set S is the union of the segment [1, 1] and the segment [3, 4], therefore S = \{ 1, 3, 4 \} holds.

There are 4 possible ways to get to Cell 5:

1 \to 2 \to 3 \to 4 \to 5,

1 \to 2 \to 5,

1 \to 4 \to 5 and

1 \to 5.

Sample Input 2

5 2
3 3
5 5

Sample Output 2

0

Because S = \{ 3, 5 \} holds, you cannot reach to Cell 5.
Print 0.

Sample Input 3

5 1
1 2

Sample Output 3

5

Sample Input 4

60 3
5 8
1 3
10 15

Sample Output 4

221823067

Note that you have to print the answer modulo 998244353.

Solution in Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main
{
	static int MOD = (int) 1e9 + 7;
	
	static class FenwickTree
	{
		// bit[1] ~ bit[n]
		long[] bit;   // = new long[n+1];
		
		public FenwickTree(int n)
		{
			bit = new long[n+1];
		}
		
		// bit[1] + ... + bit[r]
		long sum(int r)
		{
			long s = 0;
			for( int i=r; i>0; i-=(i & -i) )
			{
				s += bit[i];
			}
			return s;
		}
		
		void add(int idx, int x)
		{
			for( int i=idx; i<bit.length; i+=(i & -i) )
			{
				bit[i] += x;
			}
		}
	}

	static class UnionFind
	{
		int[] par;
		int[] n_nodes;
		int max = 1;
		
		public UnionFind(int n)
		{
			par = new int[n];
			n_nodes = new int[n];
			for( int i=0; i<n; i++ )
			{
				par[i] = i;
				n_nodes[i] = 1;
			}
		}
		
		int root(int x)
		{
			if( par[x] == x ) return x;
			return par[x] = root(par[x]);
		}
		
		void unite(int x, int y)
		{
			int rx = root(x);
			int ry = root(y);
			if( rx == ry ) return;
			par[rx] = ry;
			n_nodes[ry] += n_nodes[rx];
			max = Math.max(max, n_nodes[ry]);
		}
		
		boolean same(int x, int y)
		{
			int rx = root(x);
			int ry = root(y);
			return rx == ry;
		}
	}
	
	static class Calc
	{
		static int gcd(int a, int b)
		{
			if( a == 0 )
			{
				return b;
			}
			return gcd(b%a, a);
		}
		
		static int ceilInt(int a, int b)
		{
			return (a%b==0 ? a/b : a/b+1);
		}

		static long power(long x, int n)
		{
			if( n == 0 )
			{
				return 1;
			}

			if( n % 2 == 0 )
			{
				long X = (x * x) % MOD;
				return power(X, n/2);
			}
			else
			{
				return (x * power(x, n-1)) % MOD;
			}
		}
	}
	
	static class MyScanner
	{
		private BufferedReader in;
		private StringTokenizer st;
		
		public MyScanner(InputStream stream)
		{
			in = new BufferedReader(new InputStreamReader(stream));
		}
		
		public String next()
		{
			while( st == null || !st.hasMoreTokens() )
			{
				try
				{
					String rl = in.readLine();
					if( rl == null )
					{
						return null;
					}
					st = new StringTokenizer(rl);
				}
				catch( IOException e )
				{
					return null;
				}
			}
			return st.nextToken();
		}
		
		public int nextInt()
		{
			return Integer.parseInt(next());
		}
		
		public long nextLong()
		{
			return Long.parseLong(next());
		}
	}
	
	static interface Solver
	{
		public void solve(int testNumber, MyScanner in, PrintWriter out);
	}
	
	static class F implements Solver
	{
		public void solve(int testNumber, MyScanner in, PrintWriter out)
		{
		}
	}

	static class E implements Solver
	{
		public void solve(int testNumber, MyScanner in, PrintWriter out)
		{
		}
	}

	static class D implements Solver
	{
		long mod = 998244353;
		long[] dp;
		boolean[] flags;

		public void solve(int testNumber, MyScanner in, PrintWriter out)
		{
			int n = in.nextInt();
			int k = in.nextInt();
			flags = new boolean[n+1];

			for( int i=0; i<k; i++ )
			{
				int l = in.nextInt();
				int r = in.nextInt();
				for( int j=l; j<=r; j++ )
				{
					flags[j] = true;
				}
			}
			int[] set = new int[n+1];
			int length = 0;
			for( int i=1; i<=n; i++ )
			{
				if( flags[i] )
				{
					set[length++] = i;
				}
			}

			dp = new long[n+1];
			dp[0] = 1;
			for( int i=1; i<n; i++ )
			{
				for( int j=0; j<length && i-set[j]>=0; j++ )
				{
					dp[i] = (dp[i] + dp[i-set[j]]) % mod;
				}
			}
			out.println(dp[n-1]);
		}
	}
	
	static class C implements Solver
	{
		public void solve(int testNumber, MyScanner in, PrintWriter out)
		{
			int n = in.nextInt();
			long ans = 0;
			for( int i=1; i<n; i++ )
			{
				int sub = n - i;
				int k;
				for( k=1; k*k<sub && k>1; k++ )
				{
					if( sub%k == 0 )
					{
						ans += 2;
					}
				}
				if( k*k == sub )
				{
					ans += 1;
				}
			}
			out.println(ans);
		}
	}
	
	static class B implements Solver
	{
		public void solve(int testNumber, MyScanner in, PrintWriter out)
		{
			int n = in.nextInt();
			int cnt = 0;
			String judge = "No";
			for( int i=0; i<n; i++ )
			{
				int a = in.nextInt();
				int b = in.nextInt();
				if( a == b )
				{
					cnt++;
					if( cnt == 3 )
					{
						judge = "Yes";
					}
				}
				else
				{
					cnt = 0;
				}
			}
			out.println(judge);
		}
	}

	static class A implements Solver
	{
		public void solve(int testNumber, MyScanner in, PrintWriter out)
		{
			String s = in.next();
			if( s.endsWith("s") )
			{
				s += "es";
			}
			else
			{
				s += "s";
			}
			out.println(s);
		}
	}
	
	public static void main(String[] args)
	{
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		MyScanner in = new MyScanner(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Solver solver = new D();
		solver.solve(1, in, out);
		out.close();
	}
}