This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
#define int long long
#define vi vector<int>
#define ii pair<int, int>
#define f first
#define s second
#define all(x) (x).begin(), (x).end()
#define P 31
#define mod 1'000'000'007
#define inf 1'000'000'000'000
#define pb push_back
#define str string
#define sz(x) (x).size()
#define vvi vector<vi>
#define fun function
#define oopt cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(false);
#define file freopen("problemname.in", "r", stdin); freopen("pr.out", "w", stdout);
#define dbg(v) cout << "Line(" << __LINE__ << ") -> " << #v << " = " << (v) << endl;
using namespace std;
template <class T, int SZ> using arr = array<T, SZ>;
int b[30001];
int power[30001];
set<int> pravi[30001];
set<ii> graf[30001];
int ob[30001];
int obp[201][30001];
void solve()
{
int n, m;
cin >> n >> m;
for (int i = 0; i < 30001; i++)
{
ob[i] = inf;
for (int j = 0; j < 201; j++)
obp[j][i] = inf;
}
for (int i = 0; i < m; i++)
{
cin >> b[i] >> power[i];
if (power[i] > 200)
{
for (int j = 1; j*j <= n; j++)
{
if (b[i]+power[i]*j < n)
graf[b[i]].insert({b[i]+power[i]*j, j});
if (b[i]-power[i]*j >= 0)
graf[b[i]].insert({b[i]-power[i]*j, j});
}
}
else
{
pravi[b[i]].insert(power[i]);
}
}
priority_queue<tuple<int, int, int>, vector<tuple<int, int, int>>, greater<tuple<int, int, int>>> pq;
if (power[0] > 200)
{
pq.push({0, b[0], -1});
ob[b[0]] = 0;
}
else
{
pq.push({0, b[0], power[0]});
obp[power[0]][b[0]] = 0;
}
while (pq.size())
{
auto [d, pos, pow] = pq.top();
pq.pop();
if (pos == b[1])
{
cout << d << "\n";
return;
}
if (pow > 200 || pow == -1)
{
if (ob[pos] < d) continue;
for (auto [p, w] : graf[pos])
{
if (ob[p] > d+w)
{
ob[p] = d+w;
pq.push({d+w, p, -1});
}
}
for (int p : pravi[pos])
{
if (obp[p][pos] > d)
{
obp[p][pos] = d;
pq.push({d, pos, p});
}
}
}
else
{
if (obp[pow][pos] < d) continue;
if (pos-pow >= 0 && obp[pow][pos-pow] > d+1)
{
obp[pow][pos-pow] = d+1;
pq.push({d+1, pos-pow, pow});
}
if (pos+pow < n && obp[pow][pos+pow] > d+1)
{
obp[pow][pos+pow] = d+1;
pq.push({d+1, pos+pow, pow});
}
if (ob[pos] == 0)
{
ob[pos] = d;
pq.push({d, pos, -1});
}
for (int p : pravi[pos])
{
if (obp[p][pos] > d)
{
obp[p][pos] = d;
pq.push({d, pos, p});
}
}
}
}
cout << -1 << "\n";
}
signed main()
{
oopt;
int t = 1;
// cin >> t;
while (t--)
solve();
return 0;
}
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