Let $n$ be a natural number and $p_1^{{\alpha }_1}\cdot p_2^{{\alpha }_2}\cdots p_k^{{\alpha }_k}$ its prime factorisation.
Define the Liouville function $\lambda (n)$ as $\lambda (n)=(-1{)}^{\sum _{i=1}^k{\alpha }_i}$.
(i.e. $-1$ if the sum of the exponents ${\alpha }_i$ is odd and $1$ if the sum of the exponents is even. )
Let $S(n,L,H)$ be the sum $\lambda (d)\cdot d$ over all divisors $d$ of $n$ for which $L\le d\le H$.

You are given:

• $S(10!,100,1000)=1457$
• $S(15!,{10}^3,{10}^5)=-107974$
• $S(30!,{10}^8,{10}^{12})=9766732243224$.

Find $S(70!,{10}^{20},{10}^{60})$ and give your answer modulo $1000000007$.