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

$$t=\sum _{l=1}^{\mathrm{\infty }}\{\frac{(-1{)}^{l-1}}{l}\sum _{r=0}^{\mathrm{\infty }}\frac{1}{l{2}^r+1}\}$$
and n,k is given, caculate

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

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

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

$(1\le n\le {10}^{18},0\le k\le 30)$