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문제

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.

입력

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 ai (1 ≤ ai ≤ 1 000 000 for 1 ≤ in), separated by single spaces and denoting the quantities of balloons of respective colours. The third line of input contains m integers bi (1 ≤ bi ≤ 1 000 000 for 1 ≤ im), separated by single spaces and denoting the orders of respective children; bi = k means that the i-th child would like to buy k balloons, all having different colours.

출력

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.

예제 입력 1

4 3
3 2 1 3
1 3 4

예제 출력 1

TAK

예제 입력 2

4 3
3 2 1 3
1 4 4

예제 출력 2

NIE