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 <iostream>
using namespace std;
#define fi first
#define se second
#define ll long long int
#define pb push_back
#define MOD 998244353
int main(){
    ll a, b;
    cin>>a>>b;
    pair <ll, ll> r[b];
    for (ll i=0; i<b; i++) cin>>r[i].fi>>r[i].se;
    ll diff[2*a+2], dp[a+1];
    for (ll i=0; i<=a+1; i++) diff[i]=0;
    for (ll i=0; i<=a; i++) dp[i]=0;
    dp[1]=1;
    for (ll i=1; i<=a; i++){
        diff[i]+=diff[i-1];
        dp[i]+=diff[i];
        dp[i]%=MOD;
        for (ll j=0; j<b; j++) diff[i+r[j].fi]+=dp[i], diff[i+r[j].fi]%=MOD, diff[i+r[j].se+1]-=dp[i];
    }
    cout<<dp[a]<<endl;
}