Binary Partitions (noch nicht übersetzt)

Problem 890

Let p(n) be the number of ways to write n as the sum of powers of two, ignoring order.

For example, p(7)=6, the partitions being 7=1+1+1+1+1+1+1=1+1+1+1+1+2=1+1+1+2+2=1+1+1+4=1+2+2+2=1+2+4 You are also given p(77)144548435(mod109+7).

Find p(7777). Give your answer modulo 109+7.