请你实现三个 API append，addAll 和 multAll 来实现奇妙序列。

请实现 Fancy 类 ：

Fancy() 初始化一个空序列对象。
void append(val) 将整数 val 添加在序列末尾。
void addAll(inc) 将所有序列中的现有数值都增加 inc 。
void multAll(m) 将序列中的所有现有数值都乘以整数 m 。
int getIndex(idx) 得到下标为 idx 处的数值（下标从 0 开始），并将结果对 109 + 7 取余。如果下标大于等于序列的长度，请返回 -1 。

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/fancy-sequence
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

import java.util.Arrays;

class Fancy {

    private SegmentTree segmentTree;

    public Fancy() {
        this.segmentTree = new SegmentTree(100000);
    }

    public void append(int val) {
        segmentTree.append(val);
    }

    public void addAll(int inc) {
        segmentTree.addAll(inc);
    }

    public void multAll(int m) {
        segmentTree.multAll(m);
    }

    public int getIndex(int idx) {
        return segmentTree.getIndex(idx);
    }

    public static void main(String[] args) {
        Fancy fancy = new Fancy();
        fancy.addAll(1);   // 奇妙序列：[2+3] -> [5]
        fancy.getIndex(0); // 返回 26
    }
}

class SegmentTree {

    private static final int MOD = 1000000007;

    private int limit;

    private long[] sum;

    private long[] add;

    private long[] multiply;

    private int size;


    public SegmentTree(int limit) {
        this.limit = limit;
        this.sum = new long[limit << 2 | 1];
        this.add = new long[limit << 2 | 1];
        this.multiply = new long[limit << 2 | 1];
        Arrays.fill(multiply, 1);
    }

    private void pushUp(int rt) {
        this.sum[rt] = (this.sum[rt << 1] + this.sum[rt << 1 | 1]) % MOD;
    }

    private void pushDown(int rt, int ln, int rn) {
        if (add[rt] != 0 || multiply[rt] != 1) {
            sum[rt << 1] = (sum[rt << 1] * multiply[rt] + ln * add[rt]) % MOD;
            sum[rt << 1 | 1] = (sum[rt << 1 | 1] * multiply[rt] + rn * add[rt]) % MOD;
            multiply[rt << 1] = multiply[rt << 1] * multiply[rt] % MOD;
            multiply[rt << 1 | 1] = multiply[rt << 1 | 1] * multiply[rt] % MOD;
            add[rt << 1] = (add[rt << 1] * multiply[rt] + add[rt]) % MOD;
            add[rt << 1 | 1] = (add[rt << 1 | 1] * multiply[rt] + add[rt]) % MOD;
            multiply[rt] = 1;
            add[rt] = 0;
        }
    }

    private void multiply(int L, int R, int l, int r, int rt, int x) {
        if (L <= l && r <= R) {
            sum[rt] = sum[rt] * x % MOD;
            multiply[rt] = multiply[rt] * x % MOD;
            add[rt] = add[rt] * x % MOD;
            return;
        }
        int mid = (l + r) >> 1;
        pushDown(rt, mid - l + 1, r - mid);
        if (L <= mid) {
            multiply(L, R, l, mid, rt << 1, x);
        }
        if (mid < R) {
            multiply(L, R, mid + 1, r, rt << 1 | 1, x);
        }
        pushUp(rt);
    }

    private void add(int L, int R, int l, int r, int rt, int x) {
        if (L <= l && r <= R) {
            sum[rt] = (sum[rt] + (long) (r - l + 1) * x) % MOD;
            add[rt] = (add[rt] + x) % MOD;
            return;
        }
        int mid = (l + r) >> 1;
        pushDown(rt, mid - l + 1, r - mid);
        if (L <= mid) {
            add(L, R, l, mid, rt << 1, x);
        }
        if (mid < R) {
            add(L, R, mid + 1, r, rt << 1 | 1, x);
        }
        pushUp(rt);
    }

    private long query(int L, int R, int l, int r, int rt) {
        if (L <= l && r <= R) {
            return sum[rt];
        }
        int mid = (l + r) >> 1;
        pushDown(rt, mid - l + 1, r - mid);
        long ans = 0;
        if (L <= mid) {
            ans = (ans + query(L, R, l, mid, rt << 1)) % MOD;
        }
        if (mid < R) {
            ans = (ans + query(L, R, mid + 1, r, rt << 1 | 1)) % MOD;
        }
        return ans;
    }

    public void append(int x) {
        this.size++;
        add(this.size, this.size, 1, limit, 1, x);
    }

    public void addAll(int x) {
        if (size == 0) {
            return;
        }
        add(1, this.size, 1, limit, 1, x);
    }


    public void multAll(int x) {
        if (size == 0) {
            return;
        }
        multiply(1, this.size, 1, limit, 1, x);
    }

    public int getIndex(int index) {
        if (index >= size) {
            return -1;
        }
        return (int) query(index + 1, index + 1, 1, limit, 1);
    }
}

/**
 * Your Fancy object will be instantiated and called as such:
 * Fancy obj = new Fancy();
 * obj.append(val);
 * obj.addAll(inc);
 * obj.multAll(m);
 * int param_4 = obj.getIndex(idx);
 */