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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include <algorithm>
#include <cmath>
#include <deque>
#include <iostream>
#include <iterator>
#include <limits>
#include <map>
#include <set>
#include <string>
#include <tuple>
#include <utility>
#include <vector>

using namespace std;
using i64 = int64_t;
#define rep(i, s, n) for (i64 i = (s); i < (n); ++i)


void run() {
  const i64 mod{998244353};
  i64 n, k;
  cin >> n >> k;
  vector<i64> ls(k), rs(k);
  rep(i, 0, k){cin >> ls[i] >>rs[i];}
  vector<i64>counts(n + 1);
  vector<i64>incs(n + 1);
  incs[1] = 1;
  incs[2] = -1;
  rep(i, 1, n + 1){
    counts[i] = (counts[i - 1] + incs[i])%mod;
    rep(ik, 0, k){
      i64 il{i + ls[ik]}, ir{i + rs[ik] + 1};
      if(il < n + 1){
        incs[il] += counts[i];
        if(ir < n + 1){
          incs[ir] -= counts[i];
        }
      }
    }
  }
  cout << counts[n] << endl;
}

int main() {
  cin.tie(nullptr);
  run();
  return 0;
}