Fancy Sequence

Hard

Write an API that generates fancy sequences using the append, addAll, and multAll operations.

Build the Fancy class:

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

Example 1

Input: ["Fancy", "append", "addAll", "append", "multAll", "getIndex", "addAll", "append", "multAll", "getIndex", "getIndex", "getIndex"] [[], [2], [3], [7], [2], [0], [3], [10], [2], [0], [1], [2]]

Output: [null, null, null, null, null, 10, null, null, null, 26, 34, 20]

Explanation:

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

Constraints

1 <= val, inc, m <= 100
0 <= idx <= 10^5
At most 10^5 calls total will be made to append, addAll, multAll, and getIndex.

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