// Subroutine.
// Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
// and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
// Subroutine.
// Evaluates S = sum(N1 <= n < N2, a(n)/b(n) * (p(N1)...p(n))/(q(N1)...q(n)))
// and returns P = p(N1)...p(N2-1), Q = q(N1)...q(N2-1), B = B(N1)...B(N2-1)
}
// Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
// O(log(N)^2*M(N)).
}
// Bit complexity (if p(n), q(n), a(n), b(n) have length O(log(n))):
// O(log(N)^2*M(N)).