<s>[INST] Given a matrix with n rows and m columns, find if there is a path from the top left cell (0,0) to the bottom right cell (n-1,m-1) which satisfies the following conditions:
- The path can only be composed of 1's.
- We can move right or down at any point in time.

To solve this problem, we will extend the solution of the Nim Game problem. However, in this case, we have to turn the right moves into down moves and vice versa.

Here is a code in python that implements the above problem:

```python
def hasPath(mat):
    if not mat or not mat[0]:
        return False

    memo = {}
    def dfs(x, y):
        if (x, y) in memo:
            return memo[(x, y)]
        if x < 0 or y < 0 or x >= len(mat) or y >= len(mat[0]) or mat[x][y] != 1:
            return False
        if x == len(mat)-1 and y == len(mat[0])-1:
            return True
        memo[(x, y)] = dfs(x+1, y) or dfs(x, y+1)
        return memo[(x, y)]
    return dfs(0, 0)[/INST]