B"A polynomial A(x) of degree d is an expression of the form A(x) = a_0 + a_1 x + a_2 x^2 + ... + a_d x^d , where a_i are integers, and a_d neq 0 . Two polynomials A(x) and B(x) are called similar if there is an integer s such that for any integer x it holds that B(x) equiv A(x+s) pmod{10^9+7}. For two similar polynomials A(x) and B(x) of degree d , you're given their values in the points x=0,1, ... , d modulo 10^9+7 . Find a value s such that B(x) equiv A(x+s) pmod{10^9+7} for all integers x . The first line contains a single integer d ( 1 <= d <= 2 ,500 ,000 ). The second line contains d+1 integers A(0), A(1), ldots, A(d) ( 0 <= A(i) < 10^9+7 ) -- the values of the polynomial A(x) . The third line contains d+1 integers B(0), B(1), ldots, B(d) ( 0 <= B(i) < 10^9+7 ) -- the values of the polynomial B(x) . It is guaranteed that A(x) and B(x) are similar and that the leading coefficients (i.e., the coefficients in front of x^d ) of A(x) and B(x) are not divisible by 10^9+7 . Print a single integer s ( 0 <= q s < 10^9+7 ) such that B(x) equiv A(x+s) pmod{10^9+7} for all integers x . If there are multiple solutions, print any. In the first example, A(x) equiv x-1 pmod{10^9+7} and B(x) equiv x+2 pmod{10^9+7} . They're similar because B(x) equiv A(x+3) pmod{10^9+7}. In the second example, A(x) equiv (x+1)^2 pmod{10^9+7} and B(x) equiv (x+10)^2 pmod{10^9+7} , hence B(x) equiv A(x+9) pmod{10^9+7}. "...