Dasappa et al.'s congruence conjecture for the restricted partition function K

Let $K(n)$ be defined by its generating function

$$\sum_{n\geq 0}K(n)q^n=f_1^2f_2^2f_7^2f_{14}^2,$$

where $f_k=(q^k;q^k)_\infty$ and $(a;q)_\infty=\prod_{i\geq 0}(1-aq^i)$. Dasappa et al.'s conjecture. For all $n\geq 0$ and $\alpha\geq 1$, we have

$$K(7^\alpha n+7^\alpha-2)\equiv 0 \pmod{7^\alpha}.$$

This conjecture concerns an infinite family of congruences for a restricted color partition function introduced by Pushpa and Vasuki. The source paper states that it proves this conjecture.