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.util.*;
import java.io.*;
import java.math.*;
public class Main{
	static long mod = (int)(998244353);
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static void main(String[] args)throws IOException {
		//Scanner sc =new Scanner(System.in);
		FastReader sc = new FastReader();
		int n = sc.nextInt();
		int k = sc.nextInt();
		long dp[] = new long[n+1];
		ArrayList<Integer>	 interval = new ArrayList<>();
		
		for(int i=0;i<k;i++){
			int a = sc.nextInt();
			int b = sc.nextInt();
			for(int j=a;j<=b;j++)
				interval.add(j);
		}
		dp[1]=1;
		for(int i=2;i<=n;i++){
			for(int g : interval){
				if(i-g>=0){
					dp[i] = (dp[i-g]%mod + dp[i]%mod)%mod; 
				}
			}
		}
		System.out.println(dp[n]);
	}
	
	public static void add(TreeMap<Integer,Integer> hm, int val){
		if(!hm.containsKey(val))
			hm.put(val,1);
		else hm.put(val, hm.get(val)+1);
	}
	
	public static void remove(TreeMap<Integer,Integer> hm, int val){
		hm.put(val, hm.get(val)-1);
		if(hm.get(val)==0){
			hm.remove(val);
		}
	}
			
			
	public static long power(long a, long b){
		
		long temp = 0;
		if(b==0)
			return 1;
		
		temp = power(a, b/2);
		if(b%2==0)
			return (temp%mod*temp%mod)%mod;
		return (a%mod*(temp%mod*temp%mod)%mod)%mod;
	}
	
	public static ArrayList<Integer> primefactor(int n){
		int sqrt = (int)Math.sqrt(n);
		ArrayList<Integer> al = new ArrayList<>();
		while(n%2==0){
			al.add(2);
			n/=2;
		}
		for(int i=3;i<=sqrt;i+=2){
			while(n%i==0){
				al.add(i);
				n/=i;
			}
		}
		if(n>2)
			al.add(n);
		return al;
	}
	
	public static long sum(long val){
		long fg =0 ;
		while(val!=0){
			fg+=val%10;
			val/=10;
		}
		return fg;
	}
	
	
	
	public static ArrayList<Long> factor(long n){
		long sqrt = (long)Math.sqrt(n);
		ArrayList<Long> al = new ArrayList<>();
		for(long i=1;i<=sqrt;i++){
			if(n%i!=0)
				continue;
			long first = i;
			long second = n/i;
			al.add(i);
			if(first==second){
				continue;
			}
			al.add(n/i);
		}
		return al;
	}
	
	
	
	public static ArrayList<Integer> comp(){
		ArrayList<Integer> al = new ArrayList<>();
			int n = (int)2e5;
			boolean arr[] = new boolean[n+1];
			int sqrt = (int)Math.sqrt(n);
			for(int i=2;i<=sqrt;i++){
				if(arr[i]==false){
					for(int j=i*i;j<=n;j+=i){
						arr[j]=true;
					}
				}
			}
			for(int i=2;i<=n;i++){
				if(arr[i]==false)
					al.add(i);
			}
			
		return al;
	}
	
	public static class pair{
		int x;
		int y;
		pair(int a, int b){
			x=a;
			y=b;
		}
	}
	
	public static class comp implements Comparator<pair>{
		public int compare(pair o1, pair o2){
			return o1.x-o2.x;
		}
	}
	
	
	
	static class Node{
		int node;
		int d;
		ArrayList<Integer> al = new ArrayList<>();	
	}
	

	static int gcd(int a, int b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    }
	
		
	static class FastReader 
	{ 
		final private int BUFFER_SIZE = 1 << 16; 
		private DataInputStream din; 
		private byte[] buffer; 
		private int bufferPointer, bytesRead; 
  
		public FastReader() 
		{ 
			din = new DataInputStream(System.in); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
  
		public FastReader(String file_name) throws IOException 
		{ 
			din = new DataInputStream(new FileInputStream(file_name)); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
  
		public String readLine() throws IOException 
		{ 
			byte[] buf = new byte[64]; // line length 
			int cnt = 0, c; 
			while ((c = read()) != -1) 
			{ 
				if (c == '\n') 
					break; 
				buf[cnt++] = (byte) c; 
			} 
			return new String(buf, 0, cnt); 
		} 
  
		public int nextInt() throws IOException 
		{ 
			int ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do
			{ 
				ret = ret * 10 + c - '0'; 
			}  while ((c = read()) >= '0' && c <= '9'); 
  
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		public long nextLong() throws IOException 
		{ 
			long ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		public double nextDouble() throws IOException 
		{ 
			double ret = 0, div = 1; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
  
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
  
			if (c == '.') 
			{ 
				while ((c = read()) >= '0' && c <= '9') 
				{ 
					ret += (c - '0') / (div *= 10); 
				} 
			} 
  
			if (neg) 
				return -ret; 
			return ret; 
		} 
		
		
  
		private void fillBuffer() throws IOException 
		{ 
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
			if (bytesRead == -1) 
				buffer[0] = -1; 
		} 
  
		private byte read() throws IOException 
		{ 
			if (bufferPointer == bytesRead) 
				fillBuffer(); 
			return buffer[bufferPointer++]; 
		} 
  
		public void close() throws IOException 
		{ 
			if (din == null) 
				return; 
			din.close(); 
		} 
	} 
}