'use strict';

const PE = require('../pe_helper');

const fib    = PE.fibonacci(24);
const primes = PE.primeList(fib[24]);

const z_memo_map = {};
const p_memo_map = {};

function makeKey(n, k) {
    return `${n},${k}`;
}

// Sum of factors equal to n, smallest prime factor at least k.
function Z(n, k) {
    let key = makeKey(n, k);

    if (z_memo_map[key]) {
        return z_memo_map[key];
    }

    if (n === 0) {
        return 1;
    }

    if (n < k) {
        return 0;
    }

    let total = 0;

    for (let i = 0; i < primes.length; i++) {
        let p = primes[i];

        if (p < k) {
            continue;
        }

        if (p > n) {
            break;
        }

        total += p * Z(n - p, p);
    }

    total = total % 1e9;

    z_memo_map[key] = total;

    return total;
}

async function start() {
    for (let i = 2; i < fib[24]; i++) {
        Z(i, 2);

        // GC
        if (i % 1000 === 0) {
            console.log(i);
            await new Promise((res, rej) => setTimeout(_ => { res() }, 1));
        }
    }
}

start();

console.log(Z(fib[24], 2));