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;
constexpr ll mod=998244353;

int main()
{
  ll n,k;
  cin>>n>>k;
  vector<pair<ll,ll>> sections;
  for (int i = 0; i < k; ++i)
  {
    ll l,r;
    cin>>l>>r;
    sections.push_back({l,r});
  }
  vector<ll> f(2*n+100,0),a(2*n+100,0);
  f[1]=1;
  for (int i = 1; i < n; ++i)
  {
    for (int j = 0; j < k; ++j)
    {
      ll l=sections[j].first;
      ll r=sections[j].second;
      a[i+l]+=f[i];
      a[i+r+1]+=(mod-f[i]);
      a[i+l]%=mod;
      a[i+r+1]%=mod;
    }
    if (i==1) f[i+1]=a[i+1];
    else f[i+1]=f[i]+a[i+1];
    f[i+1]%=mod;
  }
  cout<<f[n]<<endl;
}