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)

#include <bits/stdc++.h>
using namespace std;

/* macros */
#define inf 1e9
#define int long long
#define fastio ios_base::sync_with_stdio(false);cin.tie(0);
#define vi vector<int>
#define vc vector<char>
#define vb vector<bool>
#define vt vector
#define pb push_back
#define fi first
#define se second
#define pi pair<int,int>
#define tc int t;cin>>t;while (t--){solve();}
#define gtc int t;cin>>t;int TC=1;while (t--) {cout << "Case #" << TC << ": " << solve() << "\n";TC++;}
#define gvtc int t;cin>>t;int TC=1;while (t--) {cout << "Case #" << TC << ": "; vsolve(); TC++;}
#define notc solve();
#define newline cout << "\n";
#define mod 998244353
#define ret return 0;
#define sz(x) (int)x.size();
#define rep(i,a,b) for(int i=a;i<b;i++)
#define srt(x) sort(x.begin(), x.end())
#define rsrt(x) sort(x.rbegin(), x.rend())

int n,k;
const int N = 2e5+5;
int dp[N];
int go (int pos, vi &nums) {
    if (pos == n) {
        return 1;
    }
    if (pos > n) {
        return 0;
    }
    if (dp[pos] != -1) {
        return dp[pos];
    }
    int ans = 0;
    
    for (int i=0;i<nums.size();i++) {
        ans = (ans%mod + go (pos + nums[i], nums)%mod)%mod;
    }
    
    return dp[pos] = ans;
}

void solve() {
    cin>>n>>k;
    set<int> st;
    vi nums;
    for (int i=1;i<=k;i++) {
        int l,r;
        cin>>l>>r;
        for (int j=l;j<=r;j++) {
            if (st.find(j) == st.end()) {
                st.insert(j);
                nums.push_back(j);
            }
        }
    }
    memset(dp, -1, sizeof dp);
    int ans = go (1, nums);
    cout << ans << "\n";
}

int32_t main(){
    fastio
    notc
    ret
}