A tree with N nodes is rooted at node

$1$

$$is given to you in the form of an array P

$.$

$$P

$[$

i

$]$

$$denotes the parent of the ith node. An array A is also given to you, where A

$[$

i

$]$

$$represents the number of coins present at the ith node.

you can pick some nodes as long as you follow the rules given below:

$$

$$You can pick any node at most once.

$$

$$It is given that among two nodes A and B the one with strictly lesser distance from node

$1$

$$is picked first.

$$

$$The number of coins at a chosen node is added to your score.

Find the minimum number of nodes that needs to be picked to get a score strictly greater than K

$.$

$$Output

$-$

$1$

$$if it is impossible to get a score greater than K

$.$

$$

Input format

The first line contains an integer, N

$,$

$$denoting the number of elements in P

$,$

$$The next contains an integer K

$,$

$$denoting the minimum required score,

Each line i of N subsequent lines

$($

where

$0$

$=$

$<$

$$i

$<$

$$N

$)$

$$contains an integer