AOJ2539.cpp

#include <bits/stdc++.h>

#define REP(i,n) for(int i=0;i<(int)(n);i++)
#define ALL(x) (x).begin(),(x).end()

using namespace std;

typedef long long ll;
typedef array<ll,64> Array;
typedef pair<ll,ll> P;

Array f(ll n) {
  Array res;
  res.fill(0);
  if (n <= 1) return res;
  if (n % 2) {
    res = f(n - 1);
    REP(i,64) res[i] += ((n - 1) >> i) & 1LL;
  }
  else {
    res[0] = n / 2;
    Array a = f(n / 2);
    REP(i,63) res[i+1] = a[i] * 2;
  }
  return res;
}

ll solve(const Array &ary, ll num) {
  ll sum = 0;
  int bit = 0;
  REP(i,64) if (ary[i] > 0) bit = i;
  for (int i = bit; i >= 0; --i) {
    if (ary[i] == 0) continue;
    if (num == ary[i]) sum += (1LL << i);
    else return sum + (1LL << i) + ary[i];
  }
  return sum + 1;
}

int main() {
  int n;
  while (scanf("%d", &n) && n) {
    Array ary;
    ary.fill(0);
    REP(i,n) scanf("%lld", &ary[i]);
    ll low = -1, high = -1, cnt = 0;
    for (int i = -1; i < 2; ++i) {
      ll num = ary[0] * 2 + i;
      ll h = solve(ary, num), l = h - num;
      if (l < 1 || num <= 0 || h > 1000000000000000001LL) continue;
      Array ah = f(h), lh = f(l);
      bool flag = true;
      REP(j,64) if (lh[j] + ary[j] != ah[j]) flag = false;
      if (flag) { ++cnt; low = l; high = h; }
    }
    if (cnt == 0) printf("None\n");
    else if (cnt > 1) printf("Many\n");
    else printf("%lld %lld\n", low, high-1);
  }
  return 0;
}