The task of this problem is simple: insert a sequence of distinct positive integers into a hash table, and output the positions of the input numbers. The hash function is defined to be H(key)=key%TSize where TSize is the maximum size of the hash table. Quadratic probing (with positive increments only) is used to solve the collisions.

Note that the table size is better to be prime. If the maximum size given by the user is not prime, you must re-define the table size to be the smallest prime number which is larger than the size given by the user.

Input Specification:

Each input file contains one test case. For each case, the first line contains two positive numbers: MSize (≤ 10^4 ) and N (≤MSize) which are the user-defined table size and the number of input numbers, respectively. Then N distinct positive integers are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the corresponding positions (index starts from 0) of the input numbers in one line. All the numbers in a line are separated by a space, and there must be no extra space at the end of the line. In case it is impossible to insert the number, print “-” instead.

Sample Input:

4 4
10 6 4 15

Sample Output:

0 1 4 -

注意点

• 进行二次探测时，当 step 自增达到 TSize 时如果还没有找到可用位置，则表明这个元素无法被插入。
• 创建哈希表时数组大小应该尽量比 10^4 大一些，因为当寻找大于 MSize 的最小质数时可能超过 10^4。

#include <cstdio>
#include <cmath>

const int maxn = 10010;

bool isPrime(int n) {
    if (n <= 1) {
        return false;
    } else if (n == 2) {
        return true;
    } else {
        int q = (int) sqrt(1.0 * n);
        for (int i = 2; i <= q; i++) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}

int main() {
    int tSize, n, nums[maxn] = {0}, num;
    scanf("%d %d", &tSize, &n);
    while (!isPrime(tSize)) {
        tSize++;
    }
    for (int i = 0; i < n; i++) {
        scanf("%d", &num);
        int index = num % tSize;
        if (nums[index] == 0) {
            nums[index] = num;
            if (i != 0) {
                printf(" ");
            }
            printf("%d", index);
        } else {
            int j;
            for (j = 1; j <= tSize; j++) {
                index = (num + j * j) % tSize;
                if (nums[index] == 0) {
                    nums[index] = num;
                    printf(" %d", index);
                    break;
                }
            }
            if (j > tSize) {
                printf(" -");
            }
        }
    }
    return 0;
}