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.

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 Format

The first line of input contains two integers $ n $ and $ m $ (1 ≤ $ n $ ≤ 200 000, 2 ≤ $ m $ ≤ 200 000), 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 $ n $ integers $ a_{i} $ (1 ≤ $ a_{i} $ ≤ 1 000 000 for 1 ≤ $ i $ ≤ $ n $), separated by single spaces and denoting the quantities of balloons of respective colours. The third line of input contains $ m $ integers $ b_{i} $ (1 ≤ $ b_{i} $ ≤ 1 000 000 for 1 ≤ $ i $ ≤ $ m $), separated by single spaces and denoting the orders of respective children; $ b_{i} $ = $ k $ means that the $ i $-th child would like to buy $ k $ balloons, all having different colours.

Output Format

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

Input

4 3
3 2 1 3
1 3 4

Output

TAK

Input 2

4 3
3 2 1 3
1 4 4

Output 2

NIE