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=long long;
using P=pair<ll,ll>;
static const ll mod=998244353;
ll N,K;
ll dp[200005];
ll sum[200005];
int main(){
  cin>>N>>K;
 vector<P>A(K);
  for(ll i=0;i<K;i++){
  ll l,r;cin>>l>>r;
    P p(l,r);A[i]=p;
  }
  dp[0]=1;sum[0]=1;
  for(ll i=1;i<N;i++){
    for(ll j=0;j<K;j++){
    ll l=A[j].first;ll r=A[j].second;
      if(i-l<0){}else if(0<=i-l && 0<=i-r-1){
      dp[i]=(dp[i]+sum[i-l]-sum[i-r-1]+2*mod)%mod;
      }else
        dp[i]=(dp[i]+sum[i-l])%mod;
     }sum[i]=(sum[i-1]+dp[i])%mod;
  }cout<<dp[N-1]<<endl;
    
  return 0;
}