Fancy Sequence
<p>Write an API that generates fancy sequences using the <code>append</code>, <code>addAll</code>, and <code>multAll</code> operations.</p>

<p>Implement the <code>Fancy</code> class:</p>

<ul>
	<li><code>Fancy()</code> Initializes the object with an empty sequence.</li>
	<li><code>void append(val)</code> Appends an integer <code>val</code> to the end of the sequence.</li>
	<li><code>void addAll(inc)</code> Increments all existing values in the sequence by an integer <code>inc</code>.</li>
	<li><code>void multAll(m)</code> Multiplies all existing values in the sequence by an integer <code>m</code>.</li>
	<li><code>int getIndex(idx)</code> Gets the current value at index <code>idx</code> (0-indexed) of the sequence <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>. If the index is greater or equal than the length of the sequence, return <code>-1</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;Fancy&quot;, &quot;append&quot;, &quot;addAll&quot;, &quot;append&quot;, &quot;multAll&quot;, &quot;getIndex&quot;, &quot;addAll&quot;, &quot;append&quot;, &quot;multAll&quot;, &quot;getIndex&quot;, &quot;getIndex&quot;, &quot;getIndex&quot;]
[[], [2], [3], [7], [2], [0], [3], [10], [2], [0], [1], [2]]
<strong>Output</strong>
[null, null, null, null, null, 10, null, null, null, 26, 34, 20]

<strong>Explanation</strong>
Fancy fancy = new Fancy();
fancy.append(2);   // fancy sequence: [2]
fancy.addAll(3);   // fancy sequence: [2+3] -&gt; [5]
fancy.append(7);   // fancy sequence: [5, 7]
fancy.multAll(2);  // fancy sequence: [5*2, 7*2] -&gt; [10, 14]
fancy.getIndex(0); // return 10
fancy.addAll(3);   // fancy sequence: [10+3, 14+3] -&gt; [13, 17]
fancy.append(10);  // fancy sequence: [13, 17, 10]
fancy.multAll(2);  // fancy sequence: [13*2, 17*2, 10*2] -&gt; [26, 34, 20]
fancy.getIndex(0); // return 26
fancy.getIndex(1); // return 34
fancy.getIndex(2); // return 20
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= val, inc, m &lt;= 100</code></li>
	<li><code>0 &lt;= idx &lt;= 10<sup>5</sup></code></li>
	<li>At most <code>10<sup>5</sup></code> calls total will be made to <code>append</code>, <code>addAll</code>, <code>multAll</code>, and <code>getIndex</code>.</li>
</ul>
Design; Segment Tree; Math
const int MOD = 1e9 + 7;

class Node {
public:
    Node* left;
    Node* right;
    int l;
    int r;
    int mid;
    long long v;
    long long add;
    long long mul;

    Node(int l, int r) {
        this->l = l;
        this->r = r;
        this->mid = (l + r) >> 1;
        this->left = this->right = nullptr;
        v = add = 0;
        mul = 1;
    }
};

class SegmentTree {
private:
    Node* root;

public:
    SegmentTree() {
        root = new Node(1, 1e5 + 1);
    }

    void modifyAdd(int l, int r, int inc) {
        modifyAdd(l, r, inc, root);
    }

    void modifyAdd(int l, int r, int inc, Node* node) {
        if (l > r) return;
        if (node->l >= l && node->r <= r) {
            node->v = (node->v + (node->r - node->l + 1) * inc) % MOD;
            node->add = (node->add + inc) % MOD;
            return;
        }
        pushdown(node);
        if (l <= node->mid) modifyAdd(l, r, inc, node->left);
        if (r > node->mid) modifyAdd(l, r, inc, node->right);
        pushup(node);
    }

    void modifyMul(int l, int r, int m) {
        modifyMul(l, r, m, root);
    }

    void modifyMul(int l, int r, int m, Node* node) {
        if (l > r) return;
        if (node->l >= l && node->r <= r) {
            node->v = (node->v * m) % MOD;
            node->add = (node->add * m) % MOD;
            node->mul = (node->mul * m) % MOD;
            return;
        }
        pushdown(node);
        if (l <= node->mid) modifyMul(l, r, m, node->left);
        if (r > node->mid) modifyMul(l, r, m, node->right);
        pushup(node);
    }

    int query(int l, int r) {
        return query(l, r, root);
    }

    int query(int l, int r, Node* node) {
        if (l > r) return 0;
        if (node->l >= l && node->r <= r) return node->v;
        pushdown(node);
        int v = 0;
        if (l <= node->mid) v = (v + query(l, r, node->left)) % MOD;
        if (r > node->mid) v = (v + query(l, r, node->right)) % MOD;
        return v;
    }

    void pushup(Node* node) {
        node->v = (node->left->v + node->right->v) % MOD;
    }

    void pushdown(Node* node) {
        if (!node->left) node->left = new Node(node->l, node->mid);
        if (!node->right) node->right = new Node(node->mid + 1, node->r);
        if (node->add || node->mul != 1) {
            long add = node->add, mul = node->mul;
            Node* left = node->left;
            Node* right = node->right;
            left->v = (left->v * mul + (left->r - left->l + 1) * add) % MOD;
            right->v = (right->v * mul + (right->r - right->l + 1) * add) % MOD;
            left->add = (left->add * mul + add) % MOD;
            right->add = (right->add * mul + add) % MOD;
            left->mul = (left->mul * mul) % MOD;
            right->mul = (right->mul * mul) % MOD;
            node->add = 0;
            node->mul = 1;
        }
    }
};

class Fancy {
public:
    int n;
    SegmentTree* tree;

    Fancy() {
        n = 0;
        tree = new SegmentTree();
    }

    void append(int val) {
        ++n;
        tree->modifyAdd(n, n, val);
    }

    void addAll(int inc) {
        tree->modifyAdd(1, n, inc);
    }

    void multAll(int m) {
        tree->modifyMul(1, n, m);
    }

    int getIndex(int idx) {
        return idx >= n ? -1 : tree->query(idx + 1, idx + 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);
 */