#include "bits/stdc++.h" using namespace std; #define double long double const int MAXN = 5e6 + 10; const int MOD = 1e9 + 7; mt19937_64 rng((int)std::chrono::steady_clock::now().time_since_epoch().count()); int rnd(int x, int y) { int u = uniform_int_distribution<int>(x, y)(rng); return u; } int bm(int b, int p) { if(p==0) return 1 % MOD; int r = bm(b, p >> 1); if(p&1) return (((r*r) % MOD) * b) % MOD; return (r*r) % MOD; } int inv(int b) { return bm(b, MOD-2); } int fastlog(int x) { return (x == 0 ? -1 : 64 - __builtin_clzll(x) - 1); } void printcase(int i) { cout << "Case #" << i << ": "; } vector<int>adj[MAXN]; void solve(int tc) { int n, m; cin >> n >> m; int s = sqrt(n); int b[m], p[m]; for(int i=0; i<m; i++) cin >> b[i] >> p[i]; int nxt = (s+1) * n; for(int i=1; i<=s; i++) { for(int j=i*n; j<(i+1)*n; j++) { if(j+i < (i+1)*n) adj[j].push_back((j+i) * 2 + 1); if(j-i >= i*n) adj[j].push_back((j-i) * 2 + 1); adj[j].push_back((j%n) * 2 + 0); } } for(int i=0; i<m; i++) { if(p[i] <= s) adj[b[i]].push_back((b[i]+p[i]*n) * 2 + 0); else { for(int j=b[i]%p[i]; j<n; j+=p[i]) { if(j+p[i] < n) adj[nxt + j/p[i]].push_back((nxt + j/p[i] + 1) * 2 + 1); if(j-p[i] >= 0) adj[nxt + j/p[i]].push_back((nxt + j/p[i] - 1) * 2 + 1); adj[nxt + j/p[i]].push_back(j * 2 + 0); } adj[b[i]].push_back((nxt + b[i]/p[i]) * 2 + 0); for(int j=b[i]%p[i]; j<n; j+=p[i]) { nxt++; } } } int k = nxt; int dist[k]; bool vis[k]; for(int i=0; i<k; i++) dist[i] = 1e9, vis[i] = 0; dist[b[0]] = 0; deque<int> dq; dq.push_back(b[0]); while(dq.size()) { int f = dq.front(); dq.pop_front(); if(!vis[f]) { vis[f] = 1; for(int x: adj[f]) { if(!vis[x / 2] && dist[x / 2] > dist[f] + (x % 2)) { dist[x / 2] = dist[f] + (x % 2); if(x % 2 == 0) dq.push_front(x / 2); else dq.push_back(x / 2); } } } } cout<<(dist[b[1]]==1e9?-1:dist[b[1]])<<"\n"; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); int t = 1; //cin >> t; for(int i=1; i<=t; i++) solve(i); } // 勿忘初衷