Problem:
Score : 400 points

Problem Statement

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.

Sample Input 1

5 2
1 1
3 4

Sample Output 1

4

The set S is the union of the segment [1, 1] and the segment [3, 4], therefore S = \{ 1, 3, 4 \} holds.

There are 4 possible ways to get to Cell 5:

1 \to 2 \to 3 \to 4 \to 5,

1 \to 2 \to 5,

1 \to 4 \to 5 and

1 \to 5.

Sample Input 2

5 2
3 3
5 5

Sample Output 2

0

Because S = \{ 3, 5 \} holds, you cannot reach to Cell 5.
Print 0.

Sample Input 3

5 1
1 2

Sample Output 3

5

Sample Input 4

60 3
5 8
1 3
10 15

Sample Output 4

221823067

Note that you have to print the answer modulo 998244353.

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

/* winners never quit and quitters never win.
      #swap                                 */
      
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp> 
using namespace std;
using namespace __gnu_pbds;
#pragma GCC optimize ("-O3")
using ll = long long;
using ld = long double;
const ll mod = 998244353;
const ll inf = 1000000000000000000;
const ll rk = 256;
const ld PI = 3.141592653589793;

typedef tree<
int,
null_type,
less<int>,
rb_tree_tag,
tree_order_statistics_node_update>
ordered_set;

template <typename T>
void make_unique(vector<T>& vec) {
  sort(all(vec));
  vec.erase(unique(all(vec)), vec.end());
}

#define endl '\n'
#define pb push_back
#define mp make_pair
#define vc vector
#define fs first
#define sec second
#define pq priority_queue
#define lb lower_bound
#define ub upper_bound
#define pll pair<ll,ll> 
#define pls pair<ll,string>
#define psl pair<string,ll>
#define plc pair<ll,char>
#define pcl pair<char,ll>
#define pss pair<string,string>
#define all(x) (x).begin(), (x).end()
#define tol(s) transform(s.begin(),s.end(),s.begin(),::tolower);
#define tou(s) transform(s.begin(),s.end(),s.begin(),::toupper);
#define printclock cerr<<"Time : "<<1000*(ld)clock()/(ld)CLOCKS_PER_SEC<<"ms\n";

#define error(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); }

void err(istream_iterator<string> it) {}
template<typename T, typename... Args>
void err(istream_iterator<string> it, T a, Args... args) {
	cerr << *it << " = " << a << endl;
	err(++it, args...);
}

#define rep(i, begin, end) for (__typeof(end) i = (begin) - ((begin) > (end)); i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end)))
#define T ll t=0;cin>>t;for(ll test=0;test<t;test++)

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());


ll nxt() {
    ll TemporaryVariable;
    cin >> TemporaryVariable;
    return TemporaryVariable;
}

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://xorshift.di.unimi.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

ll seg[800005],lazy[800005];
ll val;

void update(ll qlow,ll qhigh,ll low,ll high,ll pos)
{
    if(low>high)
        return;
    if(lazy[pos]!=0)
    {
        seg[pos]=(seg[pos]+lazy[pos])%mod;
        if(low!=high)
        {
            lazy[2*pos+1]=(lazy[2*pos+1]+lazy[pos])%mod;
            lazy[2*pos+2]=(lazy[2*pos+2]+lazy[pos])%mod;
        }
        lazy[pos]=0;
    }
    if(qlow>high or qhigh<low)
        return;
    if(qlow<=low and qhigh>=high)
    {
        seg[pos]=(seg[pos]+val)%mod;
        if(low!=high)
        {
            lazy[2*pos+1]=(lazy[2*pos+1]+val)%mod;
            lazy[2*pos+2]=(lazy[2*pos+2]+val)%mod;
        }
        return;
    }
    ll mid=(low+high)/2;
    update(qlow,qhigh,low,mid,2*pos+1);
    update(qlow,qhigh,mid+1,high,2*pos+2);
    seg[pos]=(seg[2*pos+1]+seg[2*pos+2])%mod;
}

ll query(ll qlow,ll qhigh,ll low,ll high,ll pos)
{
    if(low>high)
        return 0;
    if(lazy[pos]!=0)
    {
        seg[pos]=(seg[pos]+lazy[pos])%mod;
        if(low!=high)
        {
            lazy[2*pos+1]=(lazy[2*pos+1]+val)%mod;
            lazy[2*pos+2]=(lazy[2*pos+2]+val)%mod;
        }
        lazy[pos]=0;
    }
    if(qlow>high or qhigh<low)
        return 0;
    if(qlow<=low and qhigh>=high)
        return seg[pos];
    ll mid=(low+high)/2;
    return (query(qlow,qhigh,low,mid,2*pos+1)+query(qlow,qhigh,mid+1,high,2*pos+2))%mod;
}


 
int32_t main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
	//isprime();
	//coeff();
	/*freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);*/
    /*rlimit rlim;
    if (getrlimit(RLIMIT_STACK, &rlim)) return 1;
    rlim.rlim_cur = rlim.rlim_max;
    if (setrlimit(RLIMIT_STACK, &rlim)) return 2;*/
    ll n=nxt(),k=nxt();
    vc<pll> v(k);
    rep(a,0,k)
    {
        v[a].fs=nxt(),v[a].sec=nxt();
    }
    val=1;
    update(0,0,0,n-1,0);
    rep(a,0,n)
    {
        rep(b,0,k)
        {
            if(a+v[b].fs>=n)
                continue;
            ll l=a+v[b].fs,r=min(n-1,v[b].sec+a);
            val=query(a,a,0,n-1,0);
            update(l,r,0,n-1,0);
        }
    }
    cout<<query(n-1,n-1,0,n-1,0)<<endl;
	printclock;
	return 0;
}