---
id: 5900f5311000cf542c510043
title: 'Problem 452: Long Products'
challengeType: 5
forumTopicId: 302125
dashedName: problem-452-long-products
---

# --description--

Define $F(m, n)$ as the number of $n$-tuples of positive integers for which the product of the elements doesn't exceed $m$.

$F(10, 10) = 571$.

$F({10}^6, {10}^6)\bmod 1\\,234\\,567\\,891 = 252\\,903\\,833$.

Find $F({10}^9, {10}^9)\bmod 1\\,234\\,567\\,891$.

# --hints--

`longProducts()` should return `345558983`.

```js
assert.strictEqual(longProducts(), 345558983);
```

# --seed--

## --seed-contents--

```js
function longProducts() {

  return true;
}

longProducts();
```

# --solutions--

```js
// solution required
```
