HDU5312——数学——Sequence(未完成)

Today, Soda has learned a sequence whose n-th (n≥1) item is 3n(n−1)+1. Now he wants to know if an integer m can be represented as the sum of some items of that sequence. If possible, what are the minimum items needed?

For example, 22=19+1+1+1=7+7+7+1.

 

Input

There are multiple test cases. The first line of input contains an integer  T (1≤T≤104), indicating the number of test cases. For each test case:

There's a line containing an integer m (1≤m≤109).

 

Output

For each test case, output  −1 if m cannot be represented as the sum of some items of that sequence, otherwise output the minimum items needed.

 

Sample Input

10 1 2 3 4 5 6 7 8 22 10

 

Sample Output

1 2 3 4 5 6 1 2 4 4

 

Source

BestCoder 1st Anniversary ($)

 

/*

对于(n-1)%6 + 1还没想明白，等脑子清醒了再搞。。。



*/

#include <cstdio>

#include <cstring>

#include <algorithm>

using namespace std;



const int MAX = 20000;

int a[MAX];

void solve()

{

    for(int i = 0; i <= MAX; i++)

        a[i] = 3 * i * (i-1) + 1;

}

int solve(int n)

{

    int ans = n % 6;

    if(ans == 1){

        for(int i = 0 ; i <= MAX; i++){

            if(a[i] == n) return 1;

        }

        return 7;

    }

    if(ans == 2){

        int j = MAX - 1;

        for(int i = 1; i <=j; i++){

            while(a[i] + a[j] > n)

                j--;

            if(a[i] + a[j] == n)

                return 2;

        }

        return 8;

    }

    return (n - 1) % 6 + 1;

}

int main()

{

    int T, n;

    scanf("%d", &T);

    while(T--){

    scanf("%d", &n);

    printf("%d\n", solve(n));

    }

    return 0;

}