k-th Smallest Value in a Binary Search Tree

Read a binary search tree and a number k, and print the k-th smallest value in the tree, counting from 1.

How a tree is written

A tree comes on one line, read level by level and left to right. After a node come two places for its children, left first, and a child that isn't there is written null. The nulls at the very end are left out, and an empty tree is just null.

        8
      /   \
     4     11
    /     /  \
   2     9    15

This tree is written 8 4 11 2 null 9 15: first 8, then its children 4 and 11, then the children of 4 (2 and none), then those of 11 (9 and 15). The children of 2, 9 and 15 would all be null at the end, so they are left out.

In a binary search tree every value in a node's left subtree is smaller than the node's own value, every value in its right subtree is larger, and no two values are equal. The tree above is one.

The starter code already reads the input and builds the tree out of Nodes with value, left and right, then prints what kth_smallest returns. You write kth_smallest, which gets the root and k.

Input

• Line 1: a binary search tree, written as above, with 1 to 500 nodes, each value between -10^4 and 10^4.
• Line 2: k, with 1 <= k <= the number of nodes.

Output

One integer: the k-th smallest value.

Examples

Input:
8 4 11 2 null 9 15
3

Output:
8

In order the values are 2 4 8 9 11 15, and the third is 8.

Input:
8 4 11 2 null 9 15
1

Output:
2

Input:
20 10 30 null 15
2

Output:
15

The second smallest isn't always the parent of the smallest: here it is 15, the right child of 10.