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 vl=vector<ll>;
#define MOD 998244353
int main() {
    ll N; cin>>N;
    ll K; cin>>K;
    vl L(K),R(K);
    for (int i = 0; i < K; i++){
        cin>>L[i]>>R[i];
    }
    vl dp(N+1,0),sum(N+1,0);
    dp[1]=1;sum[1]=1;
    for (int i = 2; i < N+1; i++){
        for (int j = 0; j < K; j++){
            if(i-L[j]<1)continue;
            if(i-R[j]<1)dp[i]=(dp[i]+sum[i-L[j]])%MOD;
            else dp[i]=((dp[i]+sum[i-L[j]]-sum[i-R[j]-1])%MOD+MOD)%MOD;
        }
        sum[i]=(sum[i-1]+dp[i])%MOD;
    }
    cout<<dp[N]<<endl;
}