Balloons

Memory limit: 32 MB

A group of children came to a toy store. Each of them would like to buy a number of balloons. The children like diversity - none of them wants to have two balloons of the same colour. Help the shop-assistant to check whether orders of all children can be completed within the current assortment of the store.

Task

Write a program that:

• reads a description of the store's assortment and the orders made by children from the standard input,
• checks whether all children can be made happy,
• writes the result to the standard output.

Input

The first line of input contains two integers and (, ), separated by a single space and denoting the number of different colours of balloons that are present in the store and the number of children. The second line of input contains integers ( for ), separated by single spaces and denoting the quantities of balloons of respective colours. The third line of input contains integers ( for ), separated by single spaces and denoting the orders of respective children; means that the -th child would like to buy balloons, all having different colours.

Output

The first and only line of output should contain a single word TAK (i.e. yes in Polish), if orders of all children can be completed, and NIE (i.e. no in Polish) otherwise.

Example

For the input data:

4 3
3 2 1 3
1 3 4

the correct result is:

TAK

and for the input data:

4 3
3 2 1 3
1 4 4

the correct result is:

NIE

Task author: Jakub Radoszewski.