---
id: 5900f52a1000cf542c51003c
title: 'Problem 445: Retractions A'
challengeType: 5
forumTopicId: 302117
dashedName: problem-445-retractions-a
---

# --description--

For every integer n>1, the family of functions fn,a,b is defined

by fn,a,b(x)≡ax+b mod n for a,b,x integer and 0

You are given that ∑ R(c) for c=C(100 000,k), and 1 ≤ k ≤99 999 ≡628701600 (mod 1 000 000 007). (C(n,k) is the binomial coefficient).

Find ∑ R(c) for c=C(10 000 000,k), and 1 ≤k≤ 9 999 999. Give your answer modulo 1 000 000 007.

# --hints--

`euler445()` should return 659104042.

```js
assert.strictEqual(euler445(), 659104042);
```

# --seed--

## --seed-contents--

```js
function euler445() {

  return true;
}

euler445();
```

# --solutions--

```js
// solution required
```