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K Sum Paths
Medium Accuracy: 49.85% Submissions: 10981 Points: 4

Given a binary tree and an integer K. Find the number of paths in the tree which have their sum equal to K.
A path may start from any node and end at any node in the downward direction.

Example 1:

Input:
Tree =
1
/   \
2     3
K = 3
Output: 2
Explanation:
Path 1 : 1 + 2 = 3
Path 2 : only leaf node 3


Example 2:

Input:
Tree =
1
/     \
3        -1
/   \     /   \
2     1   4     5
/   / \     \
1   1   2     6
K = 5
Output: 8
Explanation:
The following paths sum to K.
3 2
3 1 1
1 3 1
4 1
1 -1 4 1
-1 4 2
5
1 -1 5 

You don't need to read input or print anything. Complete the function sumK() which takes root node and integer K as input parameters and returns the number of paths that have sum K. Since the answer may be very large, compute it modulo 109+7.

Expected Time Complexity: O(N)
Expected Auxiliary Space: O(Height of Tree)

Constraints:
1 ≤ N ≤ 105
-105 ≤ Node Value ≤ 105
-109 ≤ k ≤ 109

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