Fast array manipulation based on element inclusion in binary matrix

For a large set of randomly distributed points in a 2D lattice, I want to efficiently extract a subarray, which contains only the elements that, approximated as indices, are assigned to non-zero values in a separate 2D binary matrix. Currently, my script is the following:

lat_len = 100 # lattice length
input = np.random.random(size=(1000,2)) * lat_len
binary_matrix = np.random.choice(2, lat_len * lat_len).reshape(lat_len, -1)

def landed(input):
    output = []
    input_as_indices = np.floor(input)
    for i in range(len(input)):
        if binary_matrix[input_as_indices[i,0], input_as_indices[i,1]] == 1:
            output.append(input[i])
    output = np.asarray(output)
    return output   

However, I suspect there must be a better way of doing this. The above script can take quite long to run for 10000 iterations.