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

int main(){
  int n,k;
  cin >> n >> k;
  vector<int> a;
  vector<int> l(k);
  vector<int> r(k);
  for(int i=0;i<k;i++){
    cin >> l[i] >> r[i];
  }
  vector<long long> ans(n,0);
  ans[0]=1;
  bool f=false;
  for(int i=0;i<k;i++){
    if(l[i]==1) f=true;
  }
  if(f) ans[1]=1;
  else ans[1]=0;
  for(int i=2;i<n;i++){
    ans[i]=ans[i-1];
    for(int j=0;j<k;j++){
      if(l[j]<=i) ans[i]=ans[i]+ans[i-l[j]];
      if(r[j]+1<=i) ans[i]=ans[i]+(998244353-ans[i-r[j]-1]);
      ans[i]=ans[i]%998244353;
    }
  }
  cout << ans[n-1] << endl;
  return 0;
}