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