This problem will be judged on UESTC. Original ID: 1851
64-bit integer IO format: %lld      Java class name: Main

Prev Submit Status Statistics Discuss Next

Font Size: + -

Type:  None Graph Theory     2-SAT     Articulation/Bridge/Biconnected Component     Cycles/Topological Sorting/Strongly Connected Component     Shortest Path         Bellman Ford         Dijkstra/Floyd Warshall     Euler Trail/Circuit     Heavy-Light Decomposition     Minimum Spanning Tree     Stable Marriage Problem     Trees     Directed Minimum Spanning Tree     Flow/Matching         Graph Matching             Bipartite Matching             Hopcroft–Karp Bipartite Matching             Weighted Bipartite Matching/Hungarian Algorithm         Flow             Max Flow/Min Cut             Min Cost Max Flow DFS-like     Backtracking with Pruning/Branch and Bound     Basic Recursion     IDA* Search     Parsing/Grammar     Breadth First Search/Depth First Search     Advanced Search Techniques         Binary Search/Bisection         Ternary Search Geometry     Basic Geometry     Computational Geometry     Convex Hull     Pick's Theorem Game Theory     Green Hackenbush/Colon Principle/Fusion Principle     Nim     Sprague-Grundy Number Matrix     Gaussian Elimination     Matrix Exponentiation Data Structures     Basic Data Structures     Binary Indexed Tree     Binary Search Tree     Hashing     Orthogonal Range Search     Range Minimum Query/Lowest Common Ancestor     Segment Tree/Interval Tree     Trie Tree     Sorting     Disjoint Set String     Aho Corasick     Knuth-Morris-Pratt     Suffix Array/Suffix Tree Math     Basic Math     Big Integer Arithmetic     Number Theory         Chinese Remainder Theorem         Extended Euclid         Inclusion/Exclusion         Modular Arithmetic     Combinatorics         Group Theory/Burnside's lemma         Counting     Probability/Expected Value Others     Tricky     Hardest     Unusual     Brute Force     Implementation     Constructive Algorithms     Two Pointer     Bitmask     Beginner     Discrete Logarithm/Shank's Baby-step Giant-step Algorithm     Greedy     Divide and Conquer Dynamic Programming                   Tag it!

You are given a chessboard of size x * y and k identical kings, and are asked to place all the kings on the board such that no two kings can attack each other. Two kings can attack each other if they are horizontally, vertically or diagonally adjacent.
Write a computer program that calculates the number of possible arrangements of the k kings on the given chessboard. Since the number of feasible arrangements may be large, reduce the number modulo 1,000,000,007.

The first line of the input consists of a single integer T, the number of test cases. Each of the following T lines consists of three integers x; y and k,separated by one space.

0 < T <= 50
2 <= x; y <= 15
1 <= k <= x*y

For each test case, output the number of possibilities modulo 1,000,000,007.

4
8 8 1
7 7 16
7 7 7
3 7 15

64
1
2484382
0