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;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
int64_t MOD=998244353;
const long long INF = 1LL<<60;

int main() {
  int64_t N,K,T=0; cin>>N>>K;
  vector<int64_t> R(2*K);
  rep(i,2*K){
    cin>>R[i];
    if(i%2==1)R[i]++;
  }
  vector<int64_t> DP(N,0);
  DP[0]=1;
  for(int64_t i=0;i<N;i++){
    if(i>1)DP[i]+=DP[i-1];
    DP[i]%=MOD;
    auto k=DP[i];
    rep(j,2*K){
      auto r=R[j];
      if(i+r>=N) continue;
      if(j%2==0){
        DP[i+r]+=k;
        DP[i+r]%=MOD;
      }
      else if(j%2==1){
        DP[i+r]-=k;
      }
    }
  }
  cout<<(DP[N-1]+MOD)%MOD;
}