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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 


Your Task:  
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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