pragma solidity ^0.4.18;



contract EthPyramid {

	// scaleFactor is used to convert Ether into tokens and vice-versa: they're of different
	// orders of magnitude, hence the need to bridge between the two.
	uint256 constant scaleFactor = 0x10000000000000000;  // 2^64

	// CRR = 50%
	// CRR is Cash Reserve Ratio (in this case Crypto Reserve Ratio).
	// For more on this: check out https://en.wikipedia.org/wiki/Reserve_requirement
	int constant crr_n = 1; // CRR numerator
	int constant crr_d = 2; // CRR denominator

	// The price coefficient. Chosen such that at 1 token total supply
	// the amount in reserve is 0.5 ether and token price is 1 Ether.
	int constant price_coeff = -0x296ABF784A358468C;

	// Typical values that we have to declare.
	string constant public name = "EthPyramid";
	string constant public symbol = "EPY";
	uint8 constant public decimals = 18;

	// Array between each address and their number of tokens.
	mapping(address => uint256) public tokenBalance;
		
	// Array between each address and how much Ether has been paid out to it.
	// Note that this is scaled by the scaleFactor variable.
	mapping(address => int256) public payouts;

	// Variable tracking how many tokens are in existence overall.
	uint256 public totalSupply;

	// Aggregate sum of all payouts.
	// Note that this is scaled by the scaleFactor variable.
	int256 totalPayouts;

	// Variable tracking how much Ether each token is currently worth.
	// Note that this is scaled by the scaleFactor variable.
	uint256 earningsPerToken;
	
	// Current contract balance in Ether
	uint256 public contractBalance;

	function EthPyramid() public {}

	// The following functions are used by the front-end for display purposes.

	// Returns the number of tokens currently held by _owner.
	function balanceOf(address _owner) public constant returns (uint256 balance) {
		return tokenBalance[_owner];
	}

	// Withdraws all dividends held by the caller sending the transaction, updates
	// the requisite global variables, and transfers Ether back to the caller.
	function withdraw() public {
		// Retrieve the dividends associated with the address the request came from.
		var balance = dividends(msg.sender);
		
		// Update the payouts array, incrementing the request address by `balance`.
		payouts[msg.sender] += (int256) (balance * scaleFactor);
		
		// Increase the total amount that's been paid out to maintain invariance.
		totalPayouts += (int256) (balance * scaleFactor);
		
		// Send the dividends to the address that requested the withdraw.
		contractBalance = sub(contractBalance, balance);
		msg.sender.transfer(balance);
	}

	// Converts the Ether accrued as dividends back into EPY tokens without having to
	// withdraw it first. Saves on gas and potential price spike loss.
	function reinvestDividends() public {
		// Retrieve the dividends associated with the address the request came from.
		var balance = dividends(msg.sender);
		
		// Update the payouts array, incrementing the request address by `balance`.
		// Since this is essentially a shortcut to withdrawing and reinvesting, this step still holds.
		payouts[msg.sender] += (int256) (balance * scaleFactor);
		
		// Increase the total amount that's been paid out to maintain invariance.
		totalPayouts += (int256) (balance * scaleFactor);
		
		// Assign balance to a new variable.
		uint value_ = (uint) (balance);
		
		// If your dividends are worth less than 1 szabo, or more than a million Ether
		// (in which case, why are you even here), abort.
		if (value_ < 0.000001 ether || value_ > 1000000 ether)
			revert();
			
		// msg.sender is the address of the caller.
		var sender = msg.sender;
		
		// A temporary reserve variable used for calculating the reward the holder gets for buying tokens.
		// (Yes, the buyer receives a part of the distribution as well!)
		var res = reserve() - balance;

		// 10% of the total Ether sent is used to pay existing holders.
		var fee = div(value_, 10);
		
		// The amount of Ether used to purchase new tokens for the caller.
		var numEther = value_ - fee;
		
		// The number of tokens which can be purchased for numEther.
		var numTokens = calculateDividendTokens(numEther, balance);
		
		// The buyer fee, scaled by the scaleFactor variable.
		var buyerFee = fee * scaleFactor;
		
		// Check that we have tokens in existence (this should always be true), or
		// else you're gonna have a bad time.
		if (totalSupply > 0) {
			// Compute the bonus co-efficient for all existing holders and the buyer.
			// The buyer receives part of the distribution for each token bought in the
			// same way they would have if they bought each token individually.
			var bonusCoEff =
			    (scaleFactor - (res + numEther) * numTokens * scaleFactor / (totalSupply + numTokens) / numEther)
			    * (uint)(crr_d) / (uint)(crr_d-crr_n);
				
			// The total reward to be distributed amongst the masses is the fee (in Ether)
			// multiplied by the bonus co-efficient.
			var holderReward = fee * bonusCoEff;
			
			buyerFee -= holderReward;

			// Fee is distributed to all existing token holders before the new tokens are purchased.
			// rewardPerShare is the amount gained per token thanks to this buy-in.
			var rewardPerShare = holderReward / totalSupply;
			
			// The Ether value per token is increased proportionally.
			earningsPerToken += rewardPerShare;
		}
		
		// Add the numTokens which were just created to the total supply. We're a crypto central bank!
		totalSupply = add(totalSupply, numTokens);
		
		// Assign the tokens to the balance of the buyer.
		tokenBalance[sender] = add(tokenBalance[sender], numTokens);
		
		// Update the payout array so that the buyer cannot claim dividends on previous purchases.
		// Also include the fee paid for entering the scheme.
		// First we compute how much was just paid out to the buyer...
		var payoutDiff  = (int256) ((earningsPerToken * numTokens) - buyerFee);
		
		// Then we update the payouts array for the buyer with this amount...
		payouts[sender] += payoutDiff;
		
		// And then we finally add it to the variable tracking the total amount spent to maintain invariance.
		totalPayouts    += payoutDiff;
		
	}

	// Sells your tokens for Ether. This Ether is assigned to the callers entry
	// in the tokenBalance array, and therefore is shown as a dividend. A second
	// call to withdraw() must be made to invoke the transfer of Ether back to your address.
	function sellMyTokens() public {
		var balance = balanceOf(msg.sender);
		sell(balance);
	}

	// The slam-the-button escape hatch. Sells the callers tokens for Ether, then immediately
	// invokes the withdraw() function, sending the resulting Ether to the callers address.
    function getMeOutOfHere() public {
		sellMyTokens();
        withdraw();
	}

	// Gatekeeper function to check if the amount of Ether being sent isn't either
	// too small or too large. If it passes, goes direct to buy().
	function fund() payable public {
		// Don't allow for funding if the amount of Ether sent is less than 1 szabo.
		if (msg.value > 0.000001 ether) {
		    contractBalance = add(contractBalance, msg.value);
			buy();
		} else {
			revert();
		}
    }

	// Function that returns the (dynamic) price of buying a finney worth of tokens.
	function buyPrice() public constant returns (uint) {
		return getTokensForEther(1 finney);
	}

	// Function that returns the (dynamic) price of selling a single token.
	function sellPrice() public constant returns (uint) {
        var eth = getEtherForTokens(1 finney);
        var fee = div(eth, 10);
        return eth - fee;
    }

	// Calculate the current dividends associated with the caller address. This is the net result
	// of multiplying the number of tokens held by their current value in Ether and subtracting the
	// Ether that has already been paid out.
	function dividends(address _owner) public constant returns (uint256 amount) {
		return (uint256) ((int256)(earningsPerToken * tokenBalance[_owner]) - payouts[_owner]) / scaleFactor;
	}

	// Version of withdraw that extracts the dividends and sends the Ether to the caller.
	// This is only used in the case when there is no transaction data, and that should be
	// quite rare unless interacting directly with the smart contract.
	function withdrawOld(address to) public {
		// Retrieve the dividends associated with the address the request came from.
		var balance = dividends(msg.sender);
		
		// Update the payouts array, incrementing the request address by `balance`.
		payouts[msg.sender] += (int256) (balance * scaleFactor);
		
		// Increase the total amount that's been paid out to maintain invariance.
		totalPayouts += (int256) (balance * scaleFactor);
		
		// Send the dividends to the address that requested the withdraw.
		contractBalance = sub(contractBalance, balance);
		to.transfer(balance);		
	}

	// Internal balance function, used to calculate the dynamic reserve value.
	function balance() internal constant returns (uint256 amount) {
		// msg.value is the amount of Ether sent by the transaction.
		return contractBalance - msg.value;
	}

	function buy() internal {
		// Any transaction of less than 1 szabo is likely to be worth less than the gas used to send it.
		if (msg.value < 0.000001 ether || msg.value > 1000000 ether)
			revert();
						
		// msg.sender is the address of the caller.
		var sender = msg.sender;
		
		// 10% of the total Ether sent is used to pay existing holders.
		var fee = div(msg.value, 10);
		
		// The amount of Ether used to purchase new tokens for the caller.
		var numEther = msg.value - fee;
		
		// The number of tokens which can be purchased for numEther.
		var numTokens = getTokensForEther(numEther);
		
		// The buyer fee, scaled by the scaleFactor variable.
		var buyerFee = fee * scaleFactor;
		
		// Check that we have tokens in existence (this should always be true), or
		// else you're gonna have a bad time.
		if (totalSupply > 0) {
			// Compute the bonus co-efficient for all existing holders and the buyer.
			// The buyer receives part of the distribution for each token bought in the
			// same way they would have if they bought each token individually.
			var bonusCoEff =
			    (scaleFactor - (reserve() + numEther) * numTokens * scaleFactor / (totalSupply + numTokens) / numEther)
			    * (uint)(crr_d) / (uint)(crr_d-crr_n);
				
			// The total reward to be distributed amongst the masses is the fee (in Ether)
			// multiplied by the bonus co-efficient.
			var holderReward = fee * bonusCoEff;
			
			buyerFee -= holderReward;

			// Fee is distributed to all existing token holders before the new tokens are purchased.
			// rewardPerShare is the amount gained per token thanks to this buy-in.
			var rewardPerShare = holderReward / totalSupply;
			
			// The Ether value per token is increased proportionally.
			earningsPerToken += rewardPerShare;
			
		}

		// Add the numTokens which were just created to the total supply. We're a crypto central bank!
		totalSupply = add(totalSupply, numTokens);

		// Assign the tokens to the balance of the buyer.
		tokenBalance[sender] = add(tokenBalance[sender], numTokens);

		// Update the payout array so that the buyer cannot claim dividends on previous purchases.
		// Also include the fee paid for entering the scheme.
		// First we compute how much was just paid out to the buyer...
		var payoutDiff = (int256) ((earningsPerToken * numTokens) - buyerFee);
		
		// Then we update the payouts array for the buyer with this amount...
		payouts[sender] += payoutDiff;
		
		// And then we finally add it to the variable tracking the total amount spent to maintain invariance.
		totalPayouts    += payoutDiff;
		
	}

	// Sell function that takes tokens and converts them into Ether. Also comes with a 10% fee
	// to discouraging dumping, and means that if someone near the top sells, the fee distributed
	// will be *significant*.
	function sell(uint256 amount) internal {
	    // Calculate the amount of Ether that the holders tokens sell for at the current sell price.
		var numEthersBeforeFee = getEtherForTokens(amount);
		
		// 10% of the resulting Ether is used to pay remaining holders.
        var fee = div(numEthersBeforeFee, 10);
		
		// Net Ether for the seller after the fee has been subtracted.
        var numEthers = numEthersBeforeFee - fee;
		
		// *Remove* the numTokens which were just sold from the total supply. We're /definitely/ a crypto central bank.
		totalSupply = sub(totalSupply, amount);
		
        // Remove the tokens from the balance of the buyer.
		tokenBalance[msg.sender] = sub(tokenBalance[msg.sender], amount);

        // Update the payout array so that the seller cannot claim future dividends unless they buy back in.
		// First we compute how much was just paid out to the seller...
		var payoutDiff = (int256) (earningsPerToken * amount + (numEthers * scaleFactor));
		
        // We reduce the amount paid out to the seller (this effectively resets their payouts value to zero,
		// since they're selling all of their tokens). This makes sure the seller isn't disadvantaged if
		// they decide to buy back in.
		payouts[msg.sender] -= payoutDiff;		
		
		// Decrease the total amount that's been paid out to maintain invariance.
        totalPayouts -= payoutDiff;
		
		// Check that we have tokens in existence (this is a bit of an irrelevant check since we're
		// selling tokens, but it guards against division by zero).
		if (totalSupply > 0) {
			// Scale the Ether taken as the selling fee by the scaleFactor variable.
			var etherFee = fee * scaleFactor;
			
			// Fee is distributed to all remaining token holders.
			// rewardPerShare is the amount gained per token thanks to this sell.
			var rewardPerShare = etherFee / totalSupply;
			
			// The Ether value per token is increased proportionally.
			earningsPerToken = add(earningsPerToken, rewardPerShare);
		}
	}
	
	// Dynamic value of Ether in reserve, according to the CRR requirement.
	function reserve() internal constant returns (uint256 amount) {
		return sub(balance(),
			 ((uint256) ((int256) (earningsPerToken * totalSupply) - totalPayouts) / scaleFactor));
	}

	// Calculates the number of tokens that can be bought for a given amount of Ether, according to the
	// dynamic reserve and totalSupply values (derived from the buy and sell prices).
	function getTokensForEther(uint256 ethervalue) public constant returns (uint256 tokens) {
		return sub(fixedExp(fixedLog(reserve() + ethervalue)*crr_n/crr_d + price_coeff), totalSupply);
	}

	// Semantically similar to getTokensForEther, but subtracts the callers balance from the amount of Ether returned for conversion.
	function calculateDividendTokens(uint256 ethervalue, uint256 subvalue) public constant returns (uint256 tokens) {
		return sub(fixedExp(fixedLog(reserve() - subvalue + ethervalue)*crr_n/crr_d + price_coeff), totalSupply);
	}

	// Converts a number tokens into an Ether value.
	function getEtherForTokens(uint256 tokens) public constant returns (uint256 ethervalue) {
		// How much reserve Ether do we have left in the contract?
		var reserveAmount = reserve();

		// If you're the Highlander (or bagholder), you get The Prize. Everything left in the vault.
		if (tokens == totalSupply)
			return reserveAmount;

		// If there would be excess Ether left after the transaction this is called within, return the Ether
		// corresponding to the equation in Dr Jochen Hoenicke's original Ponzi paper, which can be found
		// at https://test.jochen-hoenicke.de/eth/ponzitoken/ in the third equation, with the CRR numerator 
		// and denominator altered to 1 and 2 respectively.
		return sub(reserveAmount, fixedExp((fixedLog(totalSupply - tokens) - price_coeff) * crr_d/crr_n));
	}

	// You don't care about these, but if you really do they're hex values for 
	// co-efficients used to simulate approximations of the log and exp functions.
	int256  constant one        = 0x10000000000000000;
	uint256 constant sqrt2      = 0x16a09e667f3bcc908;
	uint256 constant sqrtdot5   = 0x0b504f333f9de6484;
	int256  constant ln2        = 0x0b17217f7d1cf79ac;
	int256  constant ln2_64dot5 = 0x2cb53f09f05cc627c8;
	int256  constant c1         = 0x1ffffffffff9dac9b;
	int256  constant c3         = 0x0aaaaaaac16877908;
	int256  constant c5         = 0x0666664e5e9fa0c99;
	int256  constant c7         = 0x049254026a7630acf;
	int256  constant c9         = 0x038bd75ed37753d68;
	int256  constant c11        = 0x03284a0c14610924f;

	// The polynomial R = c1*x + c3*x^3 + ... + c11 * x^11
	// approximates the function log(1+x)-log(1-x)
	// Hence R(s) = log((1+s)/(1-s)) = log(a)
	function fixedLog(uint256 a) internal pure returns (int256 log) {
		int32 scale = 0;
		while (a > sqrt2) {
			a /= 2;
			scale++;
		}
		while (a <= sqrtdot5) {
			a *= 2;
			scale--;
		}
		int256 s = (((int256)(a) - one) * one) / ((int256)(a) + one);
		var z = (s*s) / one;
		return scale * ln2 +
			(s*(c1 + (z*(c3 + (z*(c5 + (z*(c7 + (z*(c9 + (z*c11/one))
				/one))/one))/one))/one))/one);
	}

	int256 constant c2 =  0x02aaaaaaaaa015db0;
	int256 constant c4 = -0x000b60b60808399d1;
	int256 constant c6 =  0x0000455956bccdd06;
	int256 constant c8 = -0x000001b893ad04b3a;
	
	// The polynomial R = 2 + c2*x^2 + c4*x^4 + ...
	// approximates the function x*(exp(x)+1)/(exp(x)-1)
	// Hence exp(x) = (R(x)+x)/(R(x)-x)
	function fixedExp(int256 a) internal pure returns (uint256 exp) {
		int256 scale = (a + (ln2_64dot5)) / ln2 - 64;
		a -= scale*ln2;
		int256 z = (a*a) / one;
		int256 R = ((int256)(2) * one) +
			(z*(c2 + (z*(c4 + (z*(c6 + (z*c8/one))/one))/one))/one);
		exp = (uint256) (((R + a) * one) / (R - a));
		if (scale >= 0)
			exp <<= scale;
		else
			exp >>= -scale;
		return exp;
	}
	
	// The below are safemath implementations of the four arithmetic operators
	// designed to explicitly prevent over- and under-flows of integer values.

	function mul(uint256 a, uint256 b) internal pure returns (uint256) {
		if (a == 0) {
			return 0;
		}
		uint256 c = a * b;
		assert(c / a == b);
		return c;
	}

	function div(uint256 a, uint256 b) internal pure returns (uint256) {
		// assert(b > 0); // Solidity automatically throws when dividing by 0
		uint256 c = a / b;
		// assert(a == b * c + a % b); // There is no case in which this doesn't hold
		return c;
	}

	function sub(uint256 a, uint256 b) internal pure returns (uint256) {
		assert(b <= a);
		return a - b;
	}

	function add(uint256 a, uint256 b) internal pure returns (uint256) {
		uint256 c = a + b;
		assert(c >= a);
		return c;
	}

	// This allows you to buy tokens by sending Ether directly to the smart contract
	// without including any transaction data (useful for, say, mobile wallet apps).
	function () payable public {
		// msg.value is the amount of Ether sent by the transaction.
		if (msg.value > 0) {
			fund();
		} else {
			withdrawOld(msg.sender);
		}
	}
}


contract DayTrader {
  // Bag sold event
  event BagSold(
    uint256 bagId,
    uint256 multiplier,
    uint256 oldPrice,
    uint256 newPrice,
    address prevOwner,
    address newOwner
  );
    address stocksaddress = 0xc6b5756b2ac3c4c3176ca4b768ae2689ff8b9cee;
    EthPyramid epc = EthPyramid(0xc6b5756b2ac3c4c3176ca4b768ae2689ff8b9cee);
        
    function epcwallet(address _t) public {
        epc = EthPyramid(_t);
    }
    
  // Address of the contract creator
  address public contractOwner;

  // Default timeout is 4 hours
  uint256 public timeout = 1 hours;

  // Default starting price is 0.005 ether
  uint256 public startingPrice = 0.005 ether;

  Bag[] private bags;

  struct Bag {
    address owner;
    uint256 level;
    uint256 multiplier; // Multiplier must be rate * 100. example: 1.5x == 150
    uint256 purchasedAt;
  }

  /// Access modifier for contract owner only functionality
  modifier onlyContractOwner() {
    require(msg.sender == contractOwner);
    _;
  }


  function DayTrader() public {
    contractOwner = msg.sender;
    createBag(150);
  }

  function createBag(uint256 multiplier) public onlyContractOwner {
    Bag memory bag = Bag({
      owner: this,
      level: 0,
      multiplier: multiplier,
      purchasedAt: 0
    });

    bags.push(bag);
  }

  function setTimeout(uint256 _timeout) public onlyContractOwner {
    timeout = _timeout;
  }
  
  function sendToStocks() public onlyContractOwner {
    stocksaddress.transfer(SafeMath.div(this.balance, 2));
  }
  
  function setStartingPrice(uint256 _startingPrice) public onlyContractOwner {
    startingPrice = _startingPrice;
  }

  function setBagMultiplier(uint256 bagId, uint256 multiplier) public onlyContractOwner {
    Bag storage bag = bags[bagId];
    bag.multiplier = multiplier;
  }

  function getBag(uint256 bagId) public view returns (
    address owner,
    uint256 sellingPrice,
    uint256 nextSellingPrice,
    uint256 level,
    uint256 multiplier,
    uint256 purchasedAt
  ) {
    Bag storage bag = bags[bagId];

    owner = bag.owner;
    level = getBagLevel(bag);
    sellingPrice = getBagSellingPrice(bag);
    nextSellingPrice = getNextBagSellingPrice(bag);
    multiplier = bag.multiplier;
    purchasedAt = bag.purchasedAt;
  }

  function getBagCount() public view returns (uint256 bagCount) {
    return bags.length;
  }

  function deleteBag(uint256 bagId) public onlyContractOwner {
    delete bags[bagId];
  }

  function purchase(uint256 bagId) public payable {
    Bag storage bag = bags[bagId];

    address oldOwner = bag.owner;
    address newOwner = msg.sender;

    // Making sure token owner is not sending to self
    require(oldOwner != newOwner);

    // Safety check to prevent against an unexpected 0x0 default.
    require(_addressNotNull(newOwner));
    
    uint256 sellingPrice = getBagSellingPrice(bag);

    // Making sure sent amount is greater than or equal to the sellingPrice
    require(msg.value >= sellingPrice);

    // Take a transaction fee
    uint256 payment = uint256(SafeMath.div(SafeMath.mul(sellingPrice, 90), 100));
    uint256 purchaseExcess = SafeMath.sub(msg.value, sellingPrice);

    uint256 level = getBagLevel(bag);
    bag.level = SafeMath.add(level, 1);
    bag.owner = newOwner;
    bag.purchasedAt = now;

    
    // Pay previous tokenOwner if owner is not contract
    if (oldOwner != address(this)) {
      oldOwner.transfer(payment);
    }

    // Trigger BagSold event
    BagSold(bagId, bag.multiplier, sellingPrice, getBagSellingPrice(bag), oldOwner, newOwner);

    newOwner.transfer(purchaseExcess);
  }

  function payout() public onlyContractOwner {
    contractOwner.transfer(this.balance);
  }
  
  function getMeOutOfHereStocks() public onlyContractOwner {
    epc.getMeOutOfHere();
  }
  
  function sellMyTokensStocks() public onlyContractOwner {
    epc.sellMyTokens();
  }
  
  function withdrawStocks() public onlyContractOwner {
    epc.withdraw();
  }
  

  /*** PRIVATE FUNCTIONS ***/

  // If a bag hasn't been purchased in over $timeout,
  // reset its level back to 0 but retain the existing owner
  function getBagLevel(Bag bag) private view returns (uint256) {
    if (now <= (SafeMath.add(bag.purchasedAt, timeout))) {
      return bag.level;
    } else {
      if(bag.level !=0)
        stocksaddress.transfer(SafeMath.div(this.balance, 2));
      return 0;
    }
  }

  function getBagSellingPrice(Bag bag) private view returns (uint256) {
    uint256 level = getBagLevel(bag);
    return getPriceForLevel(bag, level);
  }

  function getNextBagSellingPrice(Bag bag) private view returns (uint256) {
    uint256 level = SafeMath.add(getBagLevel(bag), 1);
    return getPriceForLevel(bag, level);
  }

  function getPriceForLevel(Bag bag, uint256 level) private view returns (uint256) {
    uint256 sellingPrice = startingPrice;

    for (uint256 i = 0; i < level; i++) {
      sellingPrice = SafeMath.div(SafeMath.mul(sellingPrice, bag.multiplier), 100);
    }

    return sellingPrice;
  }

  /// Safety check on _to address to prevent against an unexpected 0x0 default.
  function _addressNotNull(address _to) private pure returns (bool) {
    return _to != address(0);
  }
}

library SafeMath {

  /**
  * @dev Multiplies two numbers, throws on overflow.
  */
  function mul(uint256 a, uint256 b) internal pure returns (uint256) {
    if (a == 0) {
      return 0;
    }
    uint256 c = a * b;
    assert(c / a == b);
    return c;
  }

  /**
  * @dev Integer division of two numbers, truncating the quotient.
  */
  function div(uint256 a, uint256 b) internal pure returns (uint256) {
    // assert(b > 0); // Solidity automatically throws when dividing by 0
    uint256 c = a / b;
    // assert(a == b * c + a % b); // There is no case in which this doesn't hold
    return c;
  }

  /**
  * @dev Substracts two numbers, throws on overflow (i.e. if subtrahend is greater than minuend).
  */
  function sub(uint256 a, uint256 b) internal pure returns (uint256) {
    assert(b <= a);
    return a - b;
  }

  /**
  * @dev Adds two numbers, throws on overflow.
  */
  function add(uint256 a, uint256 b) internal pure returns (uint256) {
    uint256 c = a + b;
    assert(c >= a);
    return c;
  }
}