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> l(k),r(k);
  for(int i=0;i<k;i++){
    cin>>l[i]>>r[i];
  }
  sort(l.begin(),l.end());
  sort(r.begin(),r.end());
  vector<int64_t> a(n+1,0);
  a[1]=1;
  a[2]=-1;
  int64_t dpsum=0;
  for(int i=1;i<n;i++){
    dpsum+=a[i];
    dpsum%=998244353;
    for(int j=0;j<k;j++){
      if(i+l[j]<=n){
        a[i+l[j]]+=dpsum;
        a[i+l[j]]%=998244353;
      }
      if(i+r[j]+1<=n){
        a[i+r[j]+1]-=dpsum;
        a[i+r[j]+1]%=998244353;
      }
    }
  }
  uint64_t sum=accumulate(a.begin(),a.end(),0LL)%998244353;
  cout<<sum<<endl;
}