queryOnArray.js

// Setup.
const ARRAY_LENGTH = 8;
const STEPS = [
  [1, 1, 8],
  [0, 2, 8],
  [2, 4, 6],
  [0, 5, 6]
];

// Initial array state.
const initialArray = Array.from({ length: ARRAY_LENGTH }).fill(0);

// Helper function to check if an index is in range.
const inRange = (i, x, y) => i >= x && i <= y;

// Helper function to zero-index instruction ranges.
const zeroIndexRange = ([t, x, y]) => [t, x - 1, y - 1];

// Find the sum of all elements from index x to index y modulo 10^9+7
const sum = (x, y, arr) =>
  // Iterate over the whole array.
  arr.reduce(
    (sum, value, i) =>
      // Check if index is or is between x and y.
      inRange(i, x, y)
      // Add the current value modulo 10^9+7 to the accumulator 
      // (sum) if the index is in range. 
    	? sum + (value % (Math.pow(10, 9) + 7)) 
      // Do nothing if we are out of bounds.
    	: sum,
  0);

// Report sum and return untouched array.
const reportSum = (x, y, arr) => !console.log(sum(x, y, arr)) && arr;

// Add or subtract (controlled by modifier) (i+1)×(i+2)×(i+3) from Ax+i and so on until Ay
// This approach will suck if x-y is a lot smaler than arr.length ¯\_(ツ)_/¯
const change = (x, y, arr, modifier) =>
  // Iterate over the whole array.
  arr.map((value, i) =>
    // Check if index is or is between x and y.
    inRange(i, x, y)
      // Add (i+1)×(i+2)×(i+3)*1 or (i+1)×(i+2)×(i+3)*-1, i.e substract, to the value.
      ? value + (i - x + 1) * (i - x + 2) * (i - x + 3) * modifier
      // Leave the value untouched if we are out of bounds.
      : value
  );

// Action router.
const action = (t, x, y, arr) => {
  switch (t) {
    case 0:
      return reportSum(x, y, arr);
    case 1:
      return change(x, y, arr, 1);
    case 2:
      return change(x, y, arr, -1);
  }
};

// Recurse over steps.
const follow = (steps, arr) =>
  // Check if we still have steps to exercise.
  steps.length
    // Act on the first step in the steps array and remove it from the array.
    ? follow(steps, action(...steps.shift(), arr))
    // Return the array if there are no more steps to execute.
    : arr;

// Manipulate initial array using the steps.
const result = follow(
  // The data has ranges with one base indexs.
  // Javascript uses zero based indexs.
  // Lets change...
  STEPS.map(zeroIndexRange),
  initialArray
);