Farmer John has a pig farm near town A. He wants to visit his friend living in town B. During this journey he will visit n small villages so he decided to earn some money. He tooks n pigs and plans to sell one pig in each village he visits. Pork prices in villages are different, in the j-th village the people would buy a pork at pj rubles per kilogram. The distance from town A to the j-th village along the road to town B is dj kilometers. Pigs have different weights. Transporting one kilogram of pork per one kilometer of the road needs t rubles for addition fuel.

Help John decide, which pig to sell in each town in order to earn as much money as possible.

Input

The first line of the input file contains integer numbers n (1 ≤ n ≤ 1000) and t (1 ≤ t ≤ 10^9). The second line contains n integer numbers wi (1 ≤ wi ≤ 10^9) — the weights of the pigs. The third line contains n integer numbers dj (1 ≤ dj ≤ 10^9) — the distances to the villages from the town A. The fourth line contains n integer numbers pj (1 ≤ pj ≤ 10^9) — the prices of pork in the villages.

Output

Output n numbers, the j-th number is the number of pig to sell in the j-th village. The pigs are numbered from 1 in the order they are listed in the input file.

Sample

Input:
3 1
10 20 15
10 20 30
50 70 60

Output:
3 2 1