I tried reading the editorial but I am not getting it (may be it is too advance !). But I found that some people solved the problem in few lines can you explain the dp states
p: is the probability of getting number smaller than p ~~~~~

for (int i = 0; i <= n; ++i)
for (int j = 0; j <= n; ++j)
if (!i)
for (int a = x + j; !(a & 1); ++f[i][j], a >>= 1);
else
{
f[i][j] += f[i — 1][j + 1] * (1.0 — p);
if (!(j & 1))
f[i][j] += (f[i — 1][j / 2] + 1) * p;
}

~~~~~