In the first test case, P(0)=F2F2=22=4(mod10000019), as MEX(2,2)=0, P(1)=F1F1=11=1(mod10000019), as MEX(1,1)=1, and P(2)=F1F2=12=1(mod10000019), as MEX(1,2)=2. In the second test case, P(0)=F1F1⋅F1F2⋅F1F3⋅F2F2⋅F2F3⋅F3F3=11⋅12⋅13⋅22⋅23⋅33=864(mod10000019), as MEX(1,1)=MEX(1,2)=MEX(1,3)=MEX(2,2)=MEX(2,3)=MEX(3,3)=0, P(1)=1(mod10000019), P(2)=1(mod10000019), and P(3)=1(mod10000019). In the third test case, P(0)=F2F2⋅F4F4⋅F4F5⋅F5F5=22⋅55⋅58⋅88=2295735(mod10000019), as MEX(2,2)=MEX(4,4)=MEX(4,5)=MEX(5,5)=0, P(1)=F1F1⋅F1F2⋅F1F3⋅F2F3⋅F3F3=11⋅12⋅13⋅23⋅33=216(mod10000019), as MEX(1,1)=MEX(1,2)=MEX(1,3)=MEX(2,3)=MEX(3,3)=1, P(2)=F1F4⋅F2F4⋅F3F4=15⋅25⋅35=7776(mod10000019), as MEX(1,4)=MEX(2,4)=MEX(3,4)=2, P(3)=F3F5=38=6561(mod10000019), as MEX(3,5)=3, P(4)=F1F5⋅F2F5=18⋅28=256(mod10000019), as MEX(1,5)=MEX(2,5)=4, and P(5)=1(mod10000019). |