2014
02-24

# Another lottery

Even in times of an economic crisis, people in Byteland still like to participate in lotteries. With a bit of luck, they might get rid of all their sorrows and become rich.

The most popular lottery in Byteland consists of m rounds. In each round, everyone can purchase as many tickets as he wishes, and among all tickets sold in this round, one ticket is chosen randomly, each one with the same probability. The owner of that ticket wins the prize money of this round. Since people in Byteland like powers of 2, the prize money for the winner of round i amounts to 2i Bytelandian Dollars.

Can you determine for each participant in the lottery the probability that he will win more money than anybody else?

The input consists of several test cases. Each test case starts with a line containing two integers n and m, the number of participants in the lottery and the number of rounds in the lottery. You may assume that 1 ≤ n ≤ 10000 and 1 ≤ m ≤ 30.

The following n lines contain the description of the tickets bought by the participant. The ith such line contains m non-negative integers c1, …, cm, where cj (1 ≤ j ≤ m) is the amount of tickets of round j bought by partipant i. The total number of tickets sold in each round is between 1 and 109.

The input ends with a line containing 2 zeros.

The input consists of several test cases. Each test case starts with a line containing two integers n and m, the number of participants in the lottery and the number of rounds in the lottery. You may assume that 1 ≤ n ≤ 10000 and 1 ≤ m ≤ 30.

The following n lines contain the description of the tickets bought by the participant. The ith such line contains m non-negative integers c1, …, cm, where cj (1 ≤ j ≤ m) is the amount of tickets of round j bought by partipant i. The total number of tickets sold in each round is between 1 and 109.

The input ends with a line containing 2 zeros.

5 4
3 1 2 3
3 1 2 4
3 1 3 5
4 4 4 0
5 5 0 0
1 1
1
0 0

1 / 4
1 / 3
5 / 12
0 / 1
0 / 1
1 / 1

//BISMILLAHIRRAHMANIRRAHIM
/*
manus tar shopner soman boro
Author :: Shakil Ahmed
.............AUST_CSE27.........
prob   ::
Type   ::
verdict::
*/

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <ctype.h>
#include <math.h>
#include <limits.h>
#include <set>
#include <algorithm>
#include <iostream>
#include <vector>
#include <stack>
#include <string>
#include <list>
#include <map>
#include <queue>
#include <sstream>
#include <utility>
#define pf(a) printf("%d\n",a)
#define pf2(a,b) printf("%d %d\n",a,b)
#define pfcs(cs,a) printf("Case %d: %d\n",cs,a)
#define sc(a) scanf("%d",&a)
#define sc2(a,b) scanf("%d %d",&a,&b)
#define pb push_back
#define mp make_pair
#define pi acos(-1.0)
#define ff first
#define LL long long
#define ss second
#define rep(i,n) for(i = 0; i < n; i++)
#define REP(i,n) for(i=n;i>=0;i--)
#define FOR(i,a,b) for(int i = a; i <= b; i++)
#define ROF(i,a,b) for(int i = a; i >= b; i--)
#define re return
#define QI queue<int>
#define SI stack<int>
#define pii pair <int,int>
#define MAX
#define MOD
#define INF 1<<30
#define SZ(x) ((int) (x).size())
#define ALL(x) (x).begin(), (x).end()
#define sqr(x) ((x) * (x))
#define memo(a,b) memset((a),(b),sizeof(a))
#define G() getchar()
#define MAX3(a,b,c) max(a,max(b,c))

double const EPS=3e-8;
using namespace std;

template< class T > T gcd(T a, T b) { return (b != 0 ? gcd<T>(b, a%b) : a); }
template< class T > T lcm(T a, T b) { return (a / gcd<T>(a, b) * b); }

// Only Last RounD matter in this Problem
const int N = 10000 ;

LL Player [N];

int n,m;
void solve()
{
int i,j;
LL sum = 0,inp;
for ( i = 0 ; i < n ; i++ )
{
for ( j = 0 ; j < m-1 ; j++ ) scanf("%lld",&inp);

scanf("%lld",&Player[i]);

sum += Player[i];
}
for ( i = 0 ; i < n ; i++) {
LL g = gcd(Player[i],sum);

printf("%lld / %lld\n",Player[i]/g , sum/g );
}
}
int main()
{

//freopen("in.txt", "r", stdin);
while ( scanf ("%d %d", &n, &m) && (n + m ))
{
solve ();
}

}