CodeForces 448D Multiplication Table

D. Multiplication Table

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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 ann × 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 32 4 6

这题我搜题解了，没搜我根本不会知道这个表有个规律！！！

就是a[i][j] / i 是这一行中小于a[i][j]的数的个数。←这个这么重要不知道我还做什么啊……！！=A=

知道了之后二分就好了。如果数目大于k，移动r

#include<stdio.h>#include<string.h>__int64 n,m,k;__int64 OK(__int64 x){__int64 i;__int64 tmp,sum=0;for(i=1;i<=n;i++){tmp=x/i;if(tmp>m)tmp=m;sum+=tmp;}if(sum>=k)return 1;return 0;}int main(){while(~scanf("%I64d%I64d%I64d",&n,&m,&k)){__int64 l=1,r=n*m;__int64 mid,ans;while(l<=r){mid=(l+r)/2;if(OK(mid)){ans=mid;r=mid-1;}elsel=mid+1;}printf("%I64d\n",ans);}return 0;}