Problem:
Score : 200 points

Problem Statement

Square1001 has seen an electric bulletin board displaying the integer 1.
He can perform the following operations A and B to change this value:

Operation A: The displayed value is doubled.

Operation B: The displayed value increases by K.

Square1001 needs to perform these operations N times in total.
Find the minimum possible value displayed in the board after N operations.

Constraints

1 \leq N, K \leq 10

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
K

Output

Print the minimum possible value displayed in the board after N operations.

Sample Input 1

4
3

Sample Output 1

10

The value will be minimized when the operations are performed in the following order: A, A, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 7 → 10.

Sample Input 2

10
10

Sample Output 2

76

The value will be minimized when the operations are performed in the following order: A, A, A, A, B, B, B, B, B, B.

In this case, the value will change as follows: 1 → 2 → 4 → 8 → 16 → 26 → 36 → 46 → 56 → 66 → 76.

By the way, this contest is AtCoder Beginner Contest 076.

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
 
#define BIG 2000000007
 
#define MOD 1000000007
typedef unsigned long long ull;
typedef   signed long long sll;

#define N_MAX 200000
#define M_MAX 100
 
typedef struct {
	int a;
	int b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;
 
 
const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};
 
ull n, m;
ull h, w;
ull k;
ull va, vb, vc, vd, ve, vf;
// ull a[N_MAX];
// sll a[N_MAX];
// ull b[M_MAX];
// ull dp[N_MAX][M_MAX + 1];
char s[N_MAX + 1];
// char t[N_MAX + 1];
// char s[N_MAX][M_MAX + 1];
// hw arr[N_MAX];
// hwll arr[N_MAX];
// hw brr[M_MAX];
// ull digitdp[102][   2][    2];
//          pos  less  carry
 
void swap_adj(ull *a, ull *b){
	ull tmp = *b;
	*b = *a;
	*a = tmp;
	return;
}
 
ull divide(ull a, ull b){
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}
 
int digits(ull x){
	int i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}
 
int min(ull x, ull y){
	return (x < y) ? x : y;
}
 
ull gcd(ull x, ull y){
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}
 
ull bitpow(ull a, ull x){
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= MOD;
		}
		x /= 2;
		a = (a * a) % MOD;
	}
	return result;
}
 
// int nextroute(int arr[]){
// 	int i = n - 1;
// 	int j, x;
// 	while (arr[i - 1] > arr[i]) i--;
 
// 	x = n;
// 	for (j = i; j < n; j++) {
// 		if (arr[j] < arr[i - 1]) continue;
// 		if (x == n || arr[x] > arr[j]) x = j;
// 	}
// 	arr[i - 1] ^= arr[x];
// 	arr[x] ^= arr[i - 1];
// 	arr[i - 1] ^= arr[x];
 
// 	qsort(&arr[i], n - i, sizeof(int), comp);
// 	return 0;
// }
 
int nibutan_target(ull target){
	ull maxdist = (target * (target + 1) / 2); // 時刻targetまでに到着できる距離は[-maxdist, maxdist]
	return (n <= maxdist);
}
 
int targetdig(ull x, int index /* 1-indexed */){
	// static...?
	int posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}
 
int intcomp(const void *left, const void *right){
	if ((*(int*)left) < (*(int*)right)) {
		return -1;
	} else if ((*(int*)left) > (*(int*)right)) {
		return +1;
	} else {
		return 0;
	}
}

int ullcomp(const void *left, const void *right){
	if ((*(ull*)left) < (*(ull*)right)) {
		return -1;
	} else if ((*(ull*)left) > (*(ull*)right)) {
		return +1;
	} else {
		return 0;
	}
}

int sllcomp(const void *left, const void *right){
	if ((*(sll*)left) < (*(sll*)right)) {
		return -1;
	} else if ((*(sll*)left) > (*(sll*)right)) {
		return +1;
	} else {
		return 0;
	}
}

int hwAcomp(const void *left, const void *right){
	return intcomp(&(((hw*)left)->a), &(((hw*)right)->a));
}
 
int hwBcomp(const void *left, const void *right){
	return intcomp(&(((hw*)left)->b), &(((hw*)right)->b));
}
 
int hwABcomp(const void *left, const void *right){
	int x = hwAcomp(left, right);
	if (x) return x;
	return hwBcomp(left, right);
}

int hwllAcomp(const void *left, const void *right){
	return sllcomp(&(((hw*)left)->a), &(((hw*)right)->a));
}
 
int hwllBcomp(const void *left, const void *right){
	return sllcomp(&(((hw*)left)->b), &(((hw*)right)->b));
}
 
int hwllABcomp(const void *left, const void *right){
	int x = hwllAcomp(left, right);
	if (x) return x;
	return hwllBcomp(left, right);
}

int ispalin(int x){
	return (x == 0) || ((x & -x) == x);
}

int bitlet(char c){
	return (1 << (c - 'a'));
}

ull solve(){
	int i, j, ki;

	// ull x = (va > vb ? va - vb : vb - va);
	// ull y = (vc > vb ? vc - vb : vb - vc);

	// if (va % 2 == 1) {
	// 	puts("0");
	// } else if (x == 0 && y == 0) {
	// 	puts("-1");
	// } else {
	// 	int ans = 0;
	// 	while (x % 2 == 0 && y % 2 == 0) {
	// 		ans++;
	// 		x /= 2;
	// 		y /= 2;
	// 	}
	// 	printf("%d\n", ans);
	// }

	int len = strlen(s);

	int first = 0;
	int last = len - 1;
	int result = 0;

	int palin = 0;
	for (i = 0; i < len; i++) palin ^= bitlet(s[i]);

	while (first <= last) {
		int maylen = 0;
		int fpartlin = 0;
		int lpartlin = 0;
		for (;;) {
			if (ispalin(palin ^ fpartlin)) {
				last = first + maylen - 1;
				result++;
				palin = fpartlin;
				break;
			}
			if (ispalin(palin ^ lpartlin)) {
				first = last - maylen + 1;
				result++;
				palin = lpartlin;
				break;
			}
			fpartlin ^= bitlet(s[first + maylen]);
			lpartlin ^= bitlet(s[ last - maylen]); 
			maylen++;

		}
		printf("%d ~ %d\n", first, last);
	}

	printf("%d\n", result);

	return 0;
}
 
int main(void){
	int i, j;
	int x, y;
	int z = 1;

	// scanf("%llu", &n);
	scanf("%d%d", &x, &y);

	// solve();
	// printf("%d\n", (j * 2 - i));
	for (i = 0; i < x; i++) {
		if (z * 2 > z + y)
			z *= 2;
		else
			z += y;
	}
	printf("%d\n", z);
 
	return 0;
}