A={0,1}, everyday she will generate a binary vector randomly in. +7.Formally, it can be proved that the answer has the form of. Wcy thinks the problem too easy. Let the answer of. Note that when adding up two vectors,the components are modulo
Roundgod is obsessive about linear algebra. Let A={0,1} A={0,1}, everyday she will generate a binary vector randomly in A^n A n . Now she wonders the probability of generating n n linearly independent vectors in the next n n days modulo 10^9+7 10 9 +7. Formally, it can be proved that the answer has the form of frac{P}{Q} Q P , where P P and Q Q are coprime and Q Q is not a multiple of 10^9+7 10 9 +7. The answer modulo 10^9+7 10 9 +7 thus means P cdot Q^{-1} (textrm{mod} 10^9+7 ) P⋅Q −1 (mod 10 9 +7), where Q^{-1} Q −1 is the multiplicative inverse of 10^9+7 10 9 +7. Wcy thinks the problem too easy. Let the answer of n n be f_n f n , she wants to know f_1oplus f_2oplus ...oplus f_N f 1 ⊕f 2 ⊕...⊕f N , where oplus ⊕ denotes bitwise exclusive or operation. Note that when adding up two vectors, the components are modulo 2 2.
