bool canIWin(int maxChoosableInteger, int desiredTotal, int mask, vector<bool>& visited, vector<bool>& dp) {

if(desiredTotal <= 0) {

return false;

}

if(visited[mask]) {

return dp[mask];

}

bool canWin = false;

for(int i = 1; i <= maxChoosableInteger; i++) {

if(!(mask & (1 << i))) {

canWin |= !canIWin(maxChoosableInteger, desiredTotal - i, mask | (1 << i), visited, dp);

if(canWin) {

break;

}

}

}

visited[mask] = true;

return dp[mask] = canWin;

}

bool canIWin(int maxChoosableInteger, int desiredTotal) {

if(maxChoosableInteger >= desiredTotal) {

return true;

}

int totalPossible = (maxChoosableInteger * (maxChoosableInteger + 1)) / 2;

if(totalPossible < desiredTotal) {

return false;

}

int mask = 0;

const int maxMask = 1 << (maxChoosableInteger + 1);

vector<bool> dp(maxMask, false);

vector<bool> visited(maxMask, false);

return canIWin(maxChoosableInteger, desiredTotal, mask, visited, dp);

}