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;
using ll=int64_t;
int main(){
  ll n,k,i,j,mod=998244353;
  cin>>n>>k;
  vector<ll> l(k),r(k),dp(n),d(n);
  for(i=0;i<k;i++) cin>>l[i]>>r[i];
  dp[0]=1;
  d[1]=-1;
  for(i=0;i<n;i++){
    if(i>0) dp[i]=(dp[i-1]+d[i]+mod)%mod;
    if(i<n-1){
      for(j=0;j<k;j++){
        if(i+l[j]<n){
          d[i+l[j]]=(d[i+l[j]]+dp[i]+mod)%mod;
          if(i+r[j]+1<n) d[i+r[j]+1]=(d[i+r[j]+1]-dp[i]+mod)%mod;
        }
      }
    }
  }
  cout<<dp[n-1]<<endl;
}