---
id: 5900f5091000cf542c51001b
challengeType: 5
title: 'Problem 408: Admissible paths through a grid'
---

## Description
<section id='description'>
Let's call a lattice point (x, y) inadmissible if x, y and x + y are all positive perfect squares.
For example, (9, 16) is inadmissible, while (0, 4), (3, 1) and (9, 4) are not.

Consider a path from point (x1, y1) to point (x2, y2) using only unit steps north or east.
Let's call such a path admissible if none of its intermediate points are inadmissible.

Let P(n) be the number of admissible paths from (0, 0) to (n, n).
It can be verified that P(5) = 252, P(16) = 596994440 and P(1000) mod 1 000 000 007 = 341920854.

Find P(10 000 000) mod 1 000 000 007.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler408()</code> should return 299742733.
    testString: assert.strictEqual(euler408(), 299742733);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler408() {
  // Good luck!
  return true;
}

euler408();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>