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: Accepted)


import java.io.*;
import java.math.BigInteger;
import java.util.*;
public class Main {
	static BufferedReader br;
	static int cin() throws Exception
	{
		return Integer.valueOf(br.readLine());
	}
	static int[] split() throws Exception
	{
		String[] cmd=br.readLine().split(" ");
		int[] ans=new int[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Integer.valueOf(cmd[i]);
		}
		return ans;
	}
	static long[] splitL() throws IOException
	{
		String[] cmd=br.readLine().split(" ");
		long[] ans=new long[cmd.length];
		for(int i=0;i<cmd.length;i++)
		{
			ans[i]=Long.valueOf(cmd[i]);
		}
		return ans;
	}
	static long power(long x,long y,long p)
	{
		long res=1;
		x=x%p;
		while(y>0)
		{
			if((y&1)==1)
				res=(res*x)%p;
			y=(y>>1);
			x=(x*x)%p;
		}
		return res;
	}
	static long inv(long x,long p)
	{
		return power(x,p-2,p);
	}
	public static void main(String[] args) throws Exception{
		// TODO Auto-generated method stub
		br=new BufferedReader(new InputStreamReader(System.in));
		int[]ar=split();
		int n=ar[0];
		int k=ar[1];
		int[][]arr=new int[k][2];
		for(int i=0;i<k;i++)
		{
			ar=split();
			arr[i][0]=ar[0];
			arr[i][1]=ar[1];
		}
		int mod=998244353;
		int[]dp=new int[n];
		dp[0]=1;
		dp[1]=-1;
		for(int i=0;i<n;i++)
		{
			if(i>0)
				dp[i]=(dp[i]+dp[i-1])%mod;
			for(int j=0;j<k;j++)
			{
				int l=arr[j][0];
				int r=arr[j][1];
				if(i+l<n)
					dp[i+l]=(dp[i+l]+dp[i])%mod;
				if(i+r+1<n)
					dp[i+r+1]=((dp[i+r+1]-dp[i])%mod+mod)%mod;
			}
		}
//		int ans=0;
//		for(int i=0;i<n;i++)
//		{
//			ans=(ans+dp[i])%mod;
//		}
		System.out.println(dp[n-1]);
	}
}