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;
typedef long long ll;
#define rep(k,i,n) for(ll i=k;i<n;++i)
const ll mod=998244353;
int main(void){
    ll n,k;
    cin>>n>>k;
    vector<pair<ll,ll>>p(k);
    rep(0,i,n){
        cin>>p[i].first>>p[i].second;
    }
    ll dp[n+1],pre[n+1];
    rep(0,i,n+1){
        dp[i]=pre[i]=0;
    }
    pre[1]=1,dp[1]=1;
    rep(2,i,n+1){
        rep(0,j,k){
            ll l=p[j].first,r=p[j].second;
            if(i-l<=0)continue;
            dp[i]=(dp[i]+pre[i-l]-pre[max((ll)0,i-r-1)]+mod)%mod;
        }
        pre[i]=(dp[i]+pre[i-1])%mod;
        //cout<<dp[i]<<endl;
    }
    cout<<dp[n];
}