from fractions import *
def f(k,n):
if n <= 2:
return 0
if k < 1 or k > n:
return 0
if n == 3:
if 1 == k == 3:
return Fraction(1,3)
if k == 2:
return Fraction(-2,3)
return (Fraction(6*(k-n)*(k-1),(n-2)*(n-1)) + 1)*Fraction(30,n*(n+1)*(n+2))
temp = f(2,12)
print(temp)
print(float(temp))
ZnJvbSBmcmFjdGlvbnMgaW1wb3J0ICoKCmRlZiBmKGssbik6CiAgICBpZiBuIDw9IDI6CiAgICAgICAgcmV0dXJuIDAKICAgIGlmIGsgPCAxIG9yIGsgPiBuOgogICAgICAgIHJldHVybiAwCiAgICBpZiBuID09IDM6CiAgICAgICAgaWYgMSA9PSBrID09IDM6CiAgICAgICAgICAgIHJldHVybiBGcmFjdGlvbigxLDMpCiAgICAgICAgaWYgayA9PSAyOgogICAgICAgICAgICByZXR1cm4gRnJhY3Rpb24oLTIsMykKICAgIHJldHVybiAoRnJhY3Rpb24oNiooay1uKSooay0xKSwobi0yKSoobi0xKSkgKyAxKSpGcmFjdGlvbigzMCxuKihuKzEpKihuKzIpKQogICAgCnRlbXAgPSBmKDIsMTIpCnByaW50KHRlbXApCnByaW50KGZsb2F0KHRlbXApKQ==