Milly loves chocolates very much. She is at the land of chocolates. This land has N rooms such that there are some chocolates of different brands in every room. It is possible that there can be multiple chocolates of same brand in a particular room. Now she is in a dilemma that whether she can eat at least K distinct branded chocolates at least once. Your task is to print the minimum number of rooms she must visit to eat at least those K distinct brands at least once.

Note : Once she enters a particular room, she will eat all of the chocolates available in that room.

Input

• First line of the input will contain a integer T (number of test cases).
• Then for every test case there will be one line containing the values of N (denoting the number of rooms) and K separated by a space.
• Now each of the next N lines will first have a value P then P space separated strings denoting the names of the brands.

Output

• For every test case, print the required answer and if it is not possible to eat those K distinct chocolates then print -1.

Constraints

• 1 ≤ T ≤ 3
• 1 ≤ N ≤ 16
• 1 ≤ K ≤ 40
• 1 ≤ P ≤ 10
• 1 ≤ Length of the strings ≤ 10