Description

Windy has N balls of distinct weights from 1 unit to N units. Now he tries to label them with 1 to N in such a way that:

No two balls share the same label.

The labeling satisfies several constrains like “The ball labeled with a is lighter than the one labeled with b”.

Can you help windy to find a solution?

Input

The first line of input is the number of test case. The first line of each test case contains two integers, N (1 ≤ N ≤ 200) and M (0 ≤ M ≤ 40,000). The next M line each contain two integers a and b indicating the ball labeled with a must be lighter than the one labeled with b. (1 ≤ a, b ≤ N) There is a blank line before each test case.

Output

For each test case output on a single line the balls’ weights from label 1 to label N. If several solutions exist, you should output the one with the smallest weight for label 1, then with the smallest weight for label 2, then with the smallest weight for label 3 and so on… If no solution exists, output -1 instead.

Sample Input

Sample Output

題意

標號為 1~n 的 N 個球，滿足給定的 M 個編號約束關系，輸出最終滿足關系的球的標號。

思路

每一個標號都有可能被其他標號所約束，而對于這樣的題目我們可以聯想到拓撲排序。

但是題目要求使字典序盡可能的小，于是我們可以逆向建圖，然后從最大的標號開始判斷，因為這樣保證了大一點的標號在右邊，于是使得字典序也是最小的了。

AC 代碼