# Check if sum Y can be obtained from the Array by the given operations

Given an array of integers arr[] and two integers X and Y, the task is to check if it is possible to obtain a sequence having sum X such that the sum of each element of the subsequence multiplied by an array element is equal to Y
Note: Here X is always less than Y.

Examples:

Input: arr[] = {1, 2, 7, 9, 10}, X = 11, Y = 13
Output: Yes
Explanation:
The given value of X( = 11) can be split into a sequence {9, 2} such that 9 * 1(= arr + 2 * 2(= arr) = 13( = Y)

Input: arr[] ={1, 3, 5, 7}, X = 27, Y = 34
Output: No

Approach: Follow the steps below in order to solve the problem:

• Calculate the difference between Y and X.
• For every array element arr[i], which is > 1, update (Y – X) % (arr[i] – 1).
• If the difference is reduced 0, print “Yes“. Otherwise, print “No”.

Below is the implementation of the above approach:

 `// C++ Program to implement ` `// the above approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to check if it is possible ` `// to obtain sum Y from a sequence of ` `// sum X from the array arr[] ` `void` `solve(``int` `arr[], ``int` `n, ``int` `X, ``int` `Y) ` `{ ` ` `  `    ``// Store the difference ` `    ``int` `diff = Y - X; ` ` `  `    ``// Iterate over the array ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``if` `(arr[i] != 1) { ` `            ``diff = diff % (arr[i] - 1); ` `        ``} ` `    ``} ` ` `  `    ``// If diff reduced to 0 ` `    ``if` `(diff == 0) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 7, 9, 10 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr); ` `    ``int` `X = 11, Y = 13; ` `    ``solve(arr, n, X, Y); ` ` `  `    ``return` `0; ` `} `

 `// Java program to implement ` `// the above approach ` `class` `GFG{ ` `     `  `// Function to check if it is possible ` `// to obtain sum Y from a sequence of ` `// sum X from the array arr[] ` `static` `void` `solve(``int` `arr[], ``int` `n,  ` `                  ``int` `X, ``int` `Y) ` `{ ` `     `  `    ``// Store the difference ` `    ``int` `diff = Y - X; ` ` `  `    ``// Iterate over the array ` `    ``for``(``int` `i = ``0``; i < n; i++) ` `    ``{ ` `        ``if` `(arr[i] != ``1``)  ` `        ``{ ` `            ``diff = diff % (arr[i] - ``1``); ` `        ``} ` `    ``} ` ` `  `    ``// If diff reduced to 0 ` `    ``if` `(diff == ``0``) ` `        ``System.out.print( ``"Yes"``); ` `    ``else` `        ``System.out.print(``"No"``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String []args) ` `{ ` `    ``int` `arr[] = { ``1``, ``2``, ``7``, ``9``, ``10` `}; ` `    ``int` `n = arr.length; ` `    ``int` `X = ``11``, Y = ``13``; ` `     `  `    ``solve(arr, n, X, Y); ` `} ` `} ` ` `  `// This code is contributed by chitranayal `

 `# Python3 program to implement ` `# the above approach ` ` `  `# Function to check if it is possible ` `# to obtain sum Y from a sequence of ` `# sum X from the array arr[] ` `def` `solve(arr, n, X, Y): ` ` `  `    ``# Store the difference ` `    ``diff ``=` `Y ``-` `X ` ` `  `    ``# Iterate over the array ` `    ``for` `i ``in` `range``(n): ` `        ``if``(arr[i] !``=` `1``): ` `            ``diff ``=` `diff ``%` `(arr[i] ``-` `1``) ` ` `  `    ``# If diff reduced to 0 ` `    ``if``(diff ``=``=` `0``): ` `        ``print``(``"Yes"``) ` `    ``else``: ` `        ``print``(``"No"``) ` ` `  `# Driver Code ` `arr ``=` `[ ``1``, ``2``, ``7``, ``9``, ``10` `] ` `n ``=` `len``(arr) ` `X, Y ``=` `11``, ``13` ` `  `# Function call ` `solve(arr, n, X, Y) ` ` `  `# This code is contributed by Shivam Singh`

 `// C# program to implement ` `// the above approach ` `using` `System; ` ` `  `class` `GFG{ ` `     `  `// Function to check if it is possible ` `// to obtain sum Y from a sequence of ` `// sum X from the array []arr ` `static` `void` `solve(``int` `[]arr, ``int` `n,  ` `                  ``int` `X, ``int` `Y) ` `{ ` `     `  `    ``// Store the difference ` `    ``int` `diff = Y - X; ` ` `  `    ``// Iterate over the array ` `    ``for``(``int` `i = 0; i < n; i++) ` `    ``{ ` `        ``if` `(arr[i] != 1)  ` `        ``{ ` `            ``diff = diff % (arr[i] - 1); ` `        ``} ` `    ``} ` ` `  `    ``// If diff reduced to 0 ` `    ``if` `(diff == 0) ` `        ``Console.Write(``"Yes"``); ` `    ``else` `        ``Console.Write(``"No"``); ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``int` `[]arr = { 1, 2, 7, 9, 10 }; ` `    ``int` `n = arr.Length; ` `    ``int` `X = 11, Y = 13; ` `     `  `    ``solve(arr, n, X, Y); ` `} ` `} ` ` `  `// This code is contributed by Amit Katiyar`

Output:
```Yes
```

Time Complexity: O(N)
Auxiliary Space: O(1)

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