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 C++ (GCC 9.2.1) (judge verdict: Time Limit Exceeded)

#pragma GCC optimize("Ofast")
#pragma GCC target("avx,avx2,fma")
#pragma GCC optimization ("unroll-loops")
 
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#include <fstream>
#include<string.h>
#include <algorithm>
#include<math.h>
#include<vector>
#include <queue>
#include <deque> 
#define ll long long
#define M 1000000007 
#define MM 998244353
#define INF 4e18
using namespace std;
 
typedef tree<ll, null_type, less<int>, rb_tree_tag, 
             tree_order_statistics_node_update> 
    ordered_set; 
typedef tree<ll, null_type, less_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> indexed_multiset;

int main()
{
    std::ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    /*freopen("input.txt","r",stdin);
    freopen("output.txt","w",stdout);*/
    /*ll t,tcitr;
    cin>>t;
    tcitr=0;
    while(tcitr<t)
    {*/
        ll n,i,j,k;
        cin>>n>>k;
        ll pre[n+2]={};
        for(i=0;i<n;i++)
        {
            cin>>j>>k;
            pre[j]++;
            pre[k+1]--;
        }
        ll cnt=0;
        vector<ll> v;
        for(i=0;i<=n;i++)
        {
            cnt+=pre[i];
            if(cnt>0)v.push_back(i);
        }
        ll dp[n+1]={};
        dp[1]=1;
        for(i=1;i<=n;i++)
        {
            for(j=0;j<v.size();j++)
            {
                if(v[j]>i)break;
                dp[i]+=dp[i-v[j]];
                if(dp[i]>=MM)dp[i]-=MM;
            }
        }
        cout<<dp[n]<<"\n";
        /*tcitr++;
    }*/
    return 0;
}