thermodynamics - When the low $T$ reservoir with negative temperture (Kelvin), e.g. in Ising lattice, will the efficiency of ideal heat engine be larger than 1?

The ideal Carnot engine works between two heat reservoir with two temperatures $t_h>0$(high temperature) and $t_l>0$(low temperature). Its efficiency is then

$$\eta=1-\frac{t_l}{t_h}<1$$

For example, given the low temperature reservoir which is an infinite large Ising lattice with Hamitonian( $B>0$)

$$H= -\sum_{i} B s_i$$ with binary variable $s_i\in\{-1,1\}$. There exist configuration such that the absolute temperature of this system is negative in Kelvin.

If somehow you can couple the heat engine to the low temperature reservoir with above Ising lattice with temperature $-|t_l| < 0$), what's the efficiency of ideal Carnot engine with high temperature heat reservior $t_h>0$.