Neil and his Binary Tree CodeChef Solution – Queslers

Problem: Neil and his Binary Tree CodeChef Solution

Neil has a perfect binary tree with NN nodes, and an integer MM. He can assign values to nodes. He calls the tree good if the following conditions are met:

  • Nodes’ values are positive integers no more than MM.
  • Nodes at even levels have values strictly more than their parents’ values.
  • Nodes at odd levels have values strictly less than their parents’s values.

How many ways can Neil assign values to all nodes to get a good perfect binary tree? Since the answer can be large, please output it under modulo 109+7109+7.

Note:

  • The root of the tree is at layer 11.
  • Two assignments are different if there is at least one node with different values in both assignments.
  • You may need to use 64-bit data types in your programming language to take input.

Input Format

  • The first line of each input contains TT – the number of test cases. The test cases then follow.
  • The only line of each test case contains two space-separated integers NN and MM – the number of nodes on the tree and the maximum value of any node.

Output Format

For each test case, output on a single line the number of different assignment modulo 109+7109+7.

Constraints

  • 1≤T≤1001≤T≤100
  • 1≤M≤10001≤M≤1000
  • 1≤N<2591≤N<259
  • It is guaranteed you can make a perfect binary tree with exactly NN nodes.

Sample Input 1 

1
3 3

Sample Output 1 

5

Explanation

  • Test case 11: Here are all the possible assignments.
1-2-2
1-2-3
1-3-2
1-3-3
2-3-3
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