Problem: 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.

Examples

Input

5 2
1 1
3 4


Output

4


Input

5 2
3 3
5 5


Output

0


Input

5 1
1 2


Output

5


Input

60 3
5 8
1 3
10 15


Output

221823067

Solution (in CPP):

Solution:
#include <iostream>
#include <vector>

using namespace std;
using ll = long long;
const ll mod = 998244353;

int main() {
  int n, k;
  cin >> n >> k;
  vector<int> L(k), R(k);
  vector<ll> sum(n + 1, 0), ans(n + 1, 0);
  ans[1] = sum[1] = 1;
  for (int i = 0; i < k; i++) {
    cin >> L[i] >> R[i];
  }
  for (int i = 2; i <= n; i++) {
    for (int j = 0; j < k; j++) {
      int l = max(0, i - L[j]), r = max(0, i - R[j] - 1);

      ans[i] += sum[l] - sum[r];
      ans[i] %= mod;
    }
    ans[i] += mod;
    ans[i] %= mod;
    sum[i] = (sum[i - 1] + ans[i]) % mod;
  }
  cout << (ans[n]+mod)%mod << endl;
}