An integer is called B-smooth if none of its prime factors is greater than B.

Let S_B(n) be the largest B-smooth divisor of n.
Examples:
S₁(10) = 1
S₄(2100) = 12
S₁₇(2496144) = 5712

Define F(n) = ∑_1≤B≤n ∑_0≤r≤n S_B(C(n,r)). Here, C(n,r) denotes the binomial coefficient.
Examples:
F(11) = 3132
F(1 111) mod 1 000 000 993 = 706036312
F(111 111) mod 1 000 000 993 = 22156169

Find F(11 111 111) mod 1 000 000 993.