该函数实现将一笔钱amount按照比例ratios进行分摊，

比如100RMB按照(1,1,1)分摊的话，结果是(34,33,33)

代码如下：

public long[] allocate(long amount, long[] ratios) {
    long total = 0;
    for (int i = 0; i < ratios.length; i++) total += ratios[i];

    long remainder = amount;
    long[] results = new long[ratios.length];
    for (int i = 0; i < results.length; i++) {
        results[i] = amount * ratios[i] / total;
        remainder -= results[i];
    }

    for (int i = 0; i < remainder; i++) {
        results[i]++;
    }

    return results;
}

问题是，里面最后一个for循环，隐含着remainder<results.length，谁能给证明一下？