This problem is a special problem made by lukanel, the leader of [ 재능 ]

If you solve this problem at any time, you will become a member of [ 재능 ].

When

$$ t={\sum_{l=1}^{\infty} \{{(-1)^{l-1}\over l} \sum_{r=0}^{\infty} {1 \over l2^r+1}\}} $$
and n,k is given, caculate

$$ \phi(n)\sum_{i=1}^n [gcd(F_i,F_{X_i})\{lcm(i,i+1,{\dots},i+k)\}^t] $$

But, output it modulo $10^9+7$.

($\phi$ is Euler's totient function$\phi$$F_n$ is n’th fibonacci number, $X_n$ is n’th prime.)

$(1≤n≤10^{18}, 0≤k≤30)$