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It is shown that the low energy coefficients of the next-to-leading order(NLO) chiral perturbation theory needed to determine $\Delta I=1/2$,$K\to\pi\pi$ decay amplitudes can be fixed by calculating $K\pi\to\pi$amplitudes on lattice. Unlike using NLO $K\to\pi\pi$ amplitudes proposed byLaiho and Soni, simulating $K\pi\to\pi$ transitions on lattice does not requireevaluations of s-channel disconnected diagrams which have been an obstacle inpractice.

Next to Leading Order Chiral Perturbation theory of $K \pi \to \pi$ and $K\to\pi\pi$ amplitudes