# Form a number using corner digits of powers

Given two integers N and X. Make a number in such a way that the number contains the first and last digit occurring in .

Examples :

```Input : N = 10, X = 5
Output : 1010101010
Explanation :
10^1 = 10
10^2 = 100
10^3 = 1000
10^4 = 10000
10^5 = 100000
Take First and Last Digit of each Power to
get required number.

Input : N = 19, X = 4
Output : 19316911
Explanation :
19^1 = 19
19^2 = 361
19^3 = 6859
19^4 = 130321
Take First and Last Digit of each Power to get required number.
```

# Recommended: Please solve it on “PRACTICE“first, before moving on to the solution.

Approach :
1. Calculate all Powers of N from 1 to X one by one.
2. Store the Output in power[] array.
3. Store power i.e, last_digit and power[power_size – 1] i.e, unit_digit from power[] array to result[] array.
4. Print the result[] Array.

Below is the implementation of the above approach :

## C++

 `// C++ program to find number formed by ` `// corner digits of powers. ` `#include ` `using` `namespace` `std; ` ` `  `// Find next power by multiplying N with ` `// current power ` `void` `nextPower(``int` `N, vector<``int``> &power) ` `{ ` `    ``int` `carry = 0; ` ` `  `    ``for` `(``int` `i=0 ; i < power.size(); i++) ` `    ``{ ` `        ``int` `prod = (power[i] * N) + carry ; ` ` `  `        ``// Store digits of Power one by one. ` `        ``power[i] = prod % 10 ; ` ` `  `        ``// Calculate carry. ` `        ``carry = prod / 10 ; ` `    ``} ` ` `  `    ``while` `(carry) ` `    ``{ ` `        ``// Store carry in Power array. ` `        ``power.push_back(carry % 10); ` `        ``carry = carry / 10 ; ` `    ``} ` `} ` ` `  `// Prints number formed by corner digits of ` `// powers of N. ` `void` `printPowerNumber(``int` `X, ``int` `N) ` `{ ` `    ``// Storing N raised to power 0 ` `    ``vector<``int``> power; ` `    ``power.push_back(1); ` ` `  `    ``// Initializing empty result ` `    ``vector<``int``> res; ` ` `  `    ``// One by one compute next powers and ` `    ``// add their corner digits. ` `    ``for` `(``int` `i=1; i<=X; i++) ` `    ``{ ` `        ``// Call Fucntion that store power ` `        ``// in Power array. ` `        ``nextPower(N, power) ; ` ` `  `        ``// Store unit and last digits of ` `        ``// power in res. ` `        ``res.push_back(power.back()); ` `        ``res.push_back(power.front()); ` `    ``} ` ` `  `    ``for` `(``int` `i=0 ; i < res.size(); i++) ` `        ``cout << res[i] ; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `N = 19 , X = 4; ` `    ``printPowerNumber(X, N); ` `    ``return` `0 ; ` `} `

## Java

 `// Java program to find number formed by ` `// corner digits of powers. ` `import` `java.io.*; ` `import` `java.util.*; ` `  `  `public` `class` `GFG { ` `     `  `    ``static` `List power = ``new` `ArrayList(); ` `    ``// Find next power by multiplying N  ` `    ``// with current power ` `    ``static` `void` `nextPower(Integer N) ` `    ``{ ` `        ``Integer carry = ``0``; ` `      `  `        ``for` `(``int` `i = ``0``; i < power.size(); i++) ` `        ``{ ` `            ``Integer prod = (power.get(i) * N) + carry ; ` `      `  `            ``// Store digits of Power one by one. ` `            ``power.set(i,prod % ``10``); ` `      `  `            ``// Calculate carry. ` `            ``carry = prod / ``10` `; ` `        ``} ` `      `  `        ``while` `(carry >= ``1``) ` `        ``{ ` `            ``// Store carry in Power array. ` `            ``power.add(carry % ``10``); ` `            ``carry = carry / ``10` `; ` `        ``} ` `    ``} ` `      `  `    ``// Prints number formed by corner digits of ` `    ``// powers of N. ` `    ``static` `void` `printPowerNumber(``int` `X, ``int` `N) ` `    ``{ ` `          `  `        ``// Storing N raised to power 0 ` `        ``power.add(``1``); ` `      `  `        ``// Initializing empty result ` `        ``List res = ``new` `ArrayList(); ` `      `  `        ``// One by one compute next powers and ` `        ``// add their corner digits. ` `        ``for` `(``int` `i = ``1``; i <= X; i++) ` `        ``{ ` `            ``// Call Fucntion that store power ` `            ``// in Power array. ` `            ``nextPower(N) ; ` `      `  `            ``// Store unit and last digits of ` `            ``// power in res. ` `            ``res.add(power.get(power.size() - ``1``)); ` `            ``res.add(power.get(``0``)); ` `        ``} ` `      `  `        ``for` `(``int` `i = ``0` `; i < res.size(); i++) ` `            ``System.out.print(res.get(i)) ; ` `    ``} ` `      `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``Integer N = ``19` `, X = ``4``; ` `        ``printPowerNumber(X, N); ` `    ``} ` `} ` `  `  `// This code is contributed by Manish Shaw ` `// (manishshaw1) `

## Python3

 `# Python3 program to find  ` `# number formed by  ` `# corner digits of powers. ` `  `  `# Storing N raised to power 0 ` `power ``=` `[] ` ` `  `# Find next power by multiplying  ` `# N with current power ` `def` `nextPower(N) : ` `    ``global` `power ` `    ``carry ``=` `0` `   `  `    ``for` `i ``in` `range``(``0``, ``len``(power)) : ` `        ``prod ``=` `(power[i] ``*` `N) ``+` `carry  ` `   `  `        ``# Store digits of  ` `        ``# Power one by one. ` `        ``power[i] ``=` `prod ``%` `10`  `   `  `        ``# Calculate carry. ` `        ``carry ``=` `(``int``)(prod ``/` `10``)  ` `   `  `    ``while` `(carry) : ` ` `  `        ``# Store carry in Power array. ` `        ``power.append(carry ``%` `10``) ` `        ``carry ``=` `(``int``)(carry ``/` `10``)  ` `   `  `# Prints number formed by corner  ` `# digits of powers of N. ` `def` `printPowerNumber(X, N) : ` `    ``global` `power ` `    ``power.append(``1``) ` `   `  `    ``# Initializing empty result ` `    ``res ``=` `[] ` `   `  `    ``# One by one compute next powers  ` `    ``# and add their corner digits. ` `    ``for` `i ``in` `range``(``1``, X``+``1``) : ` ` `  `        ``# Call Fucntion that store  ` `        ``# power in Power array. ` `        ``nextPower(N)  ` `   `  `        ``# Store unit and last  ` `        ``# digits of power in res. ` `        ``res.append(power[``-``1``]) ` `        ``res.append(power[``0``]) ` `   `  `    ``for` `i ``in` `range``(``0``, ``len``(res)) : ` `        ``print` `(res[i], end``=``"")  ` `   `  `# Driver Code ` `N ``=` `19`  `X ``=` `4` `printPowerNumber(X, N) ` `   `  `# This code is contributed by  ` `# Manish Shaw(manishshaw1) `

## C#

 `// C# program to find number formed by ` `// corner digits of powers. ` `using` `System; ` `using` `System.Collections.Generic; ` `using` `System.Linq; ` `using` `System.Collections; ` ` `  `class` `GFG { ` `     `  `    ``// Find next power by multiplying N  ` `    ``// with current power ` `    ``static` `void` `nextPower(``int` `N, ``ref` `List<``int``> power) ` `    ``{ ` `        ``int` `carry = 0; ` `     `  `        ``for` `(``int` `i = 0; i < power.Count; i++) ` `        ``{ ` `            ``int` `prod = (power[i] * N) + carry ; ` `     `  `            ``// Store digits of Power one by one. ` `            ``power[i] = prod % 10 ; ` `     `  `            ``// Calculate carry. ` `            ``carry = prod / 10 ; ` `        ``} ` `     `  `        ``while` `(carry >= 1) ` `        ``{ ` `            ``// Store carry in Power array. ` `            ``power.Add(carry % 10); ` `            ``carry = carry / 10 ; ` `        ``} ` `    ``} ` `     `  `    ``// Prints number formed by corner digits of ` `    ``// powers of N. ` `    ``static` `void` `printPowerNumber(``int` `X, ``int` `N) ` `    ``{ ` `         `  `        ``// Storing N raised to power 0 ` `        ``List<``int``> power = ``new` `List<``int``>(); ` `        ``power.Add(1); ` `     `  `        ``// Initializing empty result ` `        ``List<``int``> res = ``new` `List<``int``>(); ` `     `  `        ``// One by one compute next powers and ` `        ``// add their corner digits. ` `        ``for` `(``int` `i = 1; i <= X; i++) ` `        ``{ ` `            ``// Call Fucntion that store power ` `            ``// in Power array. ` `            ``nextPower(N, ``ref` `power) ; ` `     `  `            ``// Store unit and last digits of ` `            ``// power in res. ` `            ``res.Add(power.Last()); ` `            ``res.Add(power.First()); ` `        ``} ` `     `  `        ``for` `(``int` `i = 0 ; i < res.Count; i++) ` `            ``Console.Write(res[i]) ; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `N = 19 , X = 4; ` `        ``printPowerNumber(X, N); ` `    ``} ` `} ` ` `  `// This code is contributed by Manish Shaw ` `// (manishshaw1) `

## PHP

 ` `

Output :

```19316911
```

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