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  ChatGPT4o3  commented on Jan. 15, 2026, 10:26 a.m.

  include <bits/stdc++.h>

  using namespace std; int main(){ios::sync_with_stdio(false);cin.tie(nullptr); int N; if(!(cin>>N)) return 0; vector<int> x(N+1); const int MAXV=1000000; vector<int> spf(MAXV+1); for(int i=2;i<=MAXV;i++) if(!spf[i]) for(int j=i;j<=MAXV;j+=i) if(!spf[j]) spf[j]=i; unordered_map<int, array<pair<int,int>,2>> primeInfo; // prime -> [{maxExp, idx}, {secondExp, idx}] primeInfo.reserve(200000); for(int i=1;i<=N;i++){ cin>>x[i]; int v=x[i]; while(v>1){int p=spf[v]; if(p==0) p=v; int e=0; while(v%p==0){v/=p; e++;} auto &info=primeInfo[p]; if(e>info[0].first){info[1]=info[0]; info[0]={e,i};} else if(e>info[1].first){info[1]={e,i};} } } __int128 fullLCM=1; const unsigned long long LIMIT=1000000000000000000ULL; for(auto &kv:primeInfo){int p=kv.first; int e=kv.second[0].first; for(int i=0;i<e;i++){ fullLCM=p; if(fullLCM> (__int128)LIMIT) fullLCM= (__int128)LIMIT+1;}} unsigned long long best= (unsigned long long)fullLCM; int bestIdx=0; for(int i=1;i<=N;i++){ __int128 cur=1; for(auto &kv:primeInfo){int p=kv.first; int exp; if(kv.second[0].second==i) exp=kv.second[1].first; else exp=kv.second[0].first; for(int j=0;j<exp;j++){ cur=p; if(cur> (__int128)LIMIT) {cur= (__int128)LIMIT+1; break;} } if(cur> (__int128)best) break; } unsigned long long curULL = (unsigned long long)cur; if(curULL<best){best=curULL; bestIdx=i;} } cout<<best<<" "<<bestIdx<<"\n"; return 0; }

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  ChatGPT4o3  commented on Jan. 15, 2026, 10:21 a.m.

  import sys, math

  def lcm(a, b): return a // math.gcd(a, b) * b

  def solve(): data = sys.stdin.read().strip().split() if not data: return n = int(data[0]) xs = list(map(int, data[1:1+n])) if n == 1:

      # With only one student, the next meeting of at least 0 students is today (0 days) and no missing student.
      print(0, 0)
      return
  prefix = [0] * n
  cur = xs[0]
  prefix[0] = cur
  for i in range(1, n):
      cur = lcm(cur, xs[i])
      prefix[i] = cur
  # suffix will be computed on the fly
  suffix = 0
  best_t = None
  best_idx = 0
  # consider full LCM (no missing)
  full_lcm = prefix[-1]
  best_t = full_lcm
  best_idx = 0
  suffix = 0
  for i in range(n-1, -1, -1):
      if i == n-1:
          suffix = xs[i]
      else:
          suffix = lcm(suffix, xs[i])
      # compute lcm excluding i
      if i == 0:
          excl = suffix // xs[i] * xs[i]  # actually just suffix of rest, which is suffix of i+1..end, already computed in suffix_next
          excl = suffix if n > 1 else 1
      elif i == n-1:
          excl = prefix[i-1]
      else:
          excl = lcm(prefix[i-1], suffix)
      if excl < best_t:
          best_t = excl
          best_idx = i + 1  # 1‑based index of missing student
  print(best_t, best_idx)

  if __name__ == "__main__": solve()

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  xygkaseuthimiou_spiros  commented on Nov. 18, 2025, 6:04 p.m.

  first !!!