Assign values from irregular grid points to standard grid points using interpolation

Question

I have (a lot of) data like below

y = [1, 3, 4, 5]

which corresponds to the grid points

x = [1, 2, 3, 4]

On the other hand, I have a standard grid

X = [1, 3]

What I need is to assign the value of y at x[1] = 2 and x[3] = 4, which are not in X, to the grid points in X using linear interpolation. For example, y[1] = 3 at x[1] = 2 will be allocated equally to the grid points X[0] = 1 and X[1] = 3.

The final result is expected to be

Y = [2.5, 10.5]

I have to handle millions of y and the grid points x could be different, so efficiency is important.

Any insights are appreciated.