Given a positive integer n, there exists a 0-indexed array called powers, composed of the minimum number of powers of 2 that sum to n. The array is sorted in non-decreasing order, and there is only one way to form the array. You are also given a 0-i

productQueries.js

/**
 * @param {number} n
 * @param {number[][]} queries
 * @return {number[]}
 */
var productQueries = function(n, queries) {
    const MOD = 1e9 + 7;

    // Step 1: Decompose n into powers of 2 using its binary representation
    const powers = [];
    for (let i = 0; i < 32; i++) {
        // Check if the ith bit is set
        if ((n & (1 << i)) !== 0) {
            powers.push(1 << i); // Add 2^i to the powers array
        }
    }

    // Step 2: Sort powers in non-decreasing order (though binary decomposition already gives that)
    powers.sort((a, b) => a - b);

    // Step 3: Process each query
    const answers = [];
    for (const [left, right] of queries) {
        let product = 1;
        for (let i = left; i <= right; i++) {
            product = (product * powers[i]) % MOD;
        }
        answers.push(product);
    }

    return answers;
};