---
id: 5900f5091000cf542c51001b
challengeType: 5
title: 'Problem 408: Admissible paths through a grid'
---
## 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.
## Instructions
## Tests
```yml
tests:
- text: euler408() should return 299742733.
testString: assert.strictEqual(euler408(), 299742733, 'euler408() should return 299742733.');
```
## Challenge Seed
```js
function euler408() {
// Good luck!
return true;
}
euler408();
```