Seven more than a power of two

2x+7y=k2\large 2^x + 7^y = k^2

The above equation has 2 triplets of positive integer solutions, namely (x,y,k)=(1,1,3),(x0,y0,k0)(x,y,k) = (1,1,3) , (x_0, y_0, k_0) .

Find x0+y0+k0x_0 + y_0 + k_0 .

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