#include <bits/stdc++.h>
#define hash _hash_
#define left _left_
#define y1 _y1_
using namespace std;
using ll = long long;
const ll oo = 1e18;
/*----------- I alone decide my fate! ----------*/
int N, M;
int B[30009], P[30009];
vector<pair<int,int>> adj[30009];
ll dista[30009];
void Dijkstra() {
for (int i = 0; i < M; i++) dista[i] = oo;
priority_queue<pair<ll,int>, vector<pair<ll,int>>, greater<pair<ll,int>>> pq;
dista[0] = 0;
pq.push({0, 0});
while (!pq.empty()) {
auto [cost, u] = pq.top();
pq.pop();
if (cost != dista[u]) continue;
if (u == 1) { // giữ nguyên mục tiêu như bạn viết (node index 1)
cout << cost;
return;
}
for (auto [v, w] : adj[u]) {
if (dista[v] > cost + w) {
dista[v] = cost + w;
pq.push({dista[v], v});
}
}
}
cout << -1;
}
vector<int> buckets[30009];
void solve() {
cin >> N >> M;
// reset data structures
for (int i = 0; i <= N; ++i) buckets[i].clear();
for (int i = 0; i < M; ++i) adj[i].clear();
for (int i = 0; i < M; i++) {
cin >> B[i] >> P[i];
if (P[i] <= N && P[i] >= 1) buckets[P[i]].push_back(i);
else {
// phòng trường hợp P[i] > N (không hợp lý với ý tưởng), vẫn lưu vào bucket rời
if (P[i] >= 30009) {
// rare, ignore grouping -> no edges from this node by grouping method
} else buckets[P[i]].push_back(i);
}
}
// Với mỗi p, nhóm các trạm theo (B % p), sort theo B và nối các cặp kề nhau
for (int p = 1; p <= N; ++p) {
if (buckets[p].empty()) continue;
unordered_map<int, vector<pair<int,int>>> groups;
groups.reserve(buckets[p].size()*2);
for (int idx : buckets[p]) {
int rem = B[idx] % p;
groups[rem].push_back({B[idx], idx});
}
for (auto &pr : groups) {
auto &vec = pr.second;
sort(vec.begin(), vec.end()); // sort theo B tự động
for (int k = 0; k + 1 < (int)vec.size(); ++k) {
int u = vec[k].second;
int v = vec[k+1].second;
ll delta = (ll)vec[k+1].first - (ll)vec[k].first; // khoảng cách vị trí
ll w = delta / p; // số bước (đảm bảo chia hết vì cùng class mod)
// lưu weight dưới dạng int (an toàn nếu weights nhỏ), hoặc cast cẩn thận
adj[u].push_back({v, (int)w});
adj[v].push_back({u, (int)w});
}
}
}
Dijkstra();
}
signed main() {
ios_base::sync_with_stdio(0);
cin.tie(nullptr);
solve();
return 0;
}
/*
How can you see into my eyes, like open doors?
Leading you down into my core, where I've become so numb
Without a soul, my spirit's sleeping somewhere cold
Until you find it here and bring it back home!
Wake me up! Wake me up inside
Cant wake up? Wake me up inside
*/
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