#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int maxm = 1e6 + 10;
long long n, m, k;
bool check(long long a) {
  long long tmp = 0;
  for (long long i = 1; i <= n; ++i) {
    long long b = min(a, i * m);
    tmp += b / i;
  }
  return tmp < k;
}
long long binarySearch(long long l, long long r) {
  long long mid;
  while (l < r) {
    mid = (l + r) >> 1;
    if (check(mid))
      l = mid + 1;
    else
      r = mid;
  }
  return r;
}
int main() {
  scanf("%I64d%I64d%I64d", &n, &m, &k);
  printf("%I64d\n", binarySearch(1, m * n));
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following problem:

Bizon the Champion isn't just charming, he also is very smart.

While some of us were learning the multiplication table, Bizon the Champion had fun in his own manner. Bizon the Champion painted an n × m multiplication table, where the element on the intersection of the i-th row and j-th column equals i·j (the rows and columns of the table are numbered starting from 1). Then he was asked: what number in the table is the k-th largest number? Bizon the Champion always answered correctly and immediately. Can you repeat his success?

Consider the given multiplication table. If you write out all n·m numbers from the table in the non-decreasing order, then the k-th number you write out is called the k-th largest number.

Input

The single line contains integers n, m and k (1 ≤ n, m ≤ 5·105; 1 ≤ k ≤ n·m).

Output

Print the k-th largest number in a n × m multiplication table.

Examples

Input

2 2 2


Output

2


Input

2 3 4


Output

3


Input

1 10 5


Output

5

Note

A 2 × 3 multiplication table looks like this:
    
    
      
    1 2 3  
    2 4 6  
      
    

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline int read() {
  int x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int maxm = 1e6 + 10;
long long n, m, k;
bool check(long long a) {
  long long tmp = 0;
  for (long long i = 1; i <= n; ++i) {
    long long b = min(a, i * m);
    tmp += b / i;
  }
  return tmp < k;
}
long long binarySearch(long long l, long long r) {
  long long mid;
  while (l < r) {
    mid = (l + r) >> 1;
    if (check(mid))
      l = mid + 1;
    else
      r = mid;
  }
  return r;
}
int main() {
  scanf("%I64d%I64d%I64d", &n, &m, &k);
  printf("%I64d\n", binarySearch(1, m * n));
  return 0;
}

```