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Given an undirected graph and an integer **M**. The task is to determine if the graph can be colored with at most M colors such that no two adjacent vertices of the graph are colored with the same color. Here coloring of a graph means the assignment of colors to all vertices. Print 1 if it is possible to colour vertices and 0 otherwise.

**Example 1:**

**Input:
**N = 4
M = 3
E = 5
Edges[] = {(1,2),(2,3),(3,4),(4,1),(1,3)}
**Output: **1**
Explanation: **It is possible to colour the
given graph using 3 colours.

**Example 2:**

**Input:
**N = 3
M = 2
E = 3
Edges[] = {(1,2),(2,3),(1,3)}
**Output: **0

**Your Task:**

Your task is to complete the function **graphColoring()** which takes the 2d-array graph[], the number of colours and the number of nodes as inputs and returns **true** if answer exists otherwise **false**. 1 is printed if the returned value is **true, **0 otherwise. The printing is done by the driver's code.

**Note**: In the given 2d-array graph[], if there is an edge between vertex X and vertex Y graph[] will contain 1 at graph[X-1][Y-1], else 0. In 2d-array graph[ ], nodes are 0-based indexed, i.e. from 0 to N-1.

**Expected Time Complexity:** O(M^{N}).

**Expected Auxiliary ****Space:** O(N).

**Constraints:**

1 <= N <= 20

1 <= E <= (N*(N-1))/2

1 <= M <= N

**Note: **The given inputs are 1-base indexed but you have to consider the graph given in the adjacency matrix/list as 0-base indexed.

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M-Coloring Problem

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