# Odd Long Tally Counter

**Computer Science**Level 4

**This problem is the more-evil-version of this problem.**

A normal long tally counter has \( 7 \) digits and counts \( 1 \) by \( 1 \), hence there are \( 10^{7} \) different numbers can be shown on it (in range \( 0000000 ... 9999999 \)).

Suppose you have an odd long tally counter. Instead \( 1 \) by \( 1 \), it counts \( x \) by \( x \). In case of overflow, the counter only shows the last \( 7 \) digits of the number.

For example, if \( x = 1000001 \) the counter will show these numbers : \( 0000000, 1000001, 2000002, ..., 9000009, 0000010, 1000011, ... \)

Let \( F(n) \) be the function returning the number of different numbers can be shown on odd long tally counter with \( x = n \), find the last \( 3 \) digits of \( \sum_{i=1}^{10^7-1} F(i)\).

**As an explicit example** : \( F(1) = 10^7 \)

**This problem is taken from TOKI Open Contest January 2013 (Problemsetter : Me)**

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